Used Abbreviation:
C.C. = Condensed Carbon (this is gonna get used a lot)

Infinite Di-Hydrogen:

Needed to start: 30 Di-Hydrogen
30 Di-Hydrogen -> Di-Hydrogen Jelly -> 40 Di-Hydrogen
This is very slow, but I don’t think there is another way.

Yield: 30 Di-Hydrogen -> 40 Di-Hydrogen.

Infinite Carbon (this is the basis for almost everything in this guide):

You can get infinite amounts of Carbon straight from the start just with your Portable Refiner (you need 30 Oxygen and 50 Ferrite Dust to craft that one). This is pretty slow and tedious, but it can get you started without having to harvest a ton of plants and should in most cases be faster than that for medium/large quantities.
I recommend looking for a cave and do this while getting some Cobalt etc. while the refiner is going.

Needed to start:
80 Carbon OR 27 Condensed Carbon (you can make less work if you manage to fuel it and still have some Carbon in your inventory (either harvested after fueling or having some Carbon and some C.C. or select a smaller amount to put in))
+ any amount of Carbon/C.C. for duping

How to dupe:
If you don’t have any C.C. yet, fill up your refiner with Carbon and then refine all the Carbon you have left into C.C.. From now on, always use C.C. to fuel your refiner!!!
Loop:
Fill your Portable Refiner with Condensed Carbon and pick it back up right away. The 27 C.C. you filled the refiner with have turned into 100 Carbon. Do that until you have <27 C.C. left. Once you don't have enough for a full load of fuel for your refiner, refine all the Carbon you have into C.C.
Repeat this loop, until you have as much Carbon as you want.

Yield: 27 C.C. (= 54 Carbon) -> 80 Carbon (= 50 C.C.)
(Note: update 02/23 reduced the amount you need for filling your refiner from 100 carbon / 34 C.C. to 80 carbon or 27 C.C.. This makes this slightly more efficient and you can even fill the refiner with 80 carbon and get 100 out of it upon pickup. Turning it into C.C. is still more effective, though.
I’m writing this on Feb 22nd, 2023, future updates might change this back, in case this wasn’t on purpose. There might also be an option in the new custom difficulty settings that affected this, but I didn’t see one, apart from the option to make crafting free, which I didn’t use.)

Infinite Carbon with a Medium Refiner:
Resources needed:
— Medium (/Large) Refiner
— some C.C. to get started
— 1 Di-Hydrogen OR 1 Mordite OR 3 Faecium

1 Faecium + 1 C.C. -> 3 C.C.

Create Faecium:
Use this once to get you started, unless you already have some Faecium:
1 Di-Hydrogen + 1 C.C. -> 1 Mordite
1 Mordite + 1 C.C. -> 4 Faecium
Keep a big stack of Faecium around, you’re going to need it once in a while (for example to dupe Cobalt, see Minerals for that)

Yield: 1 Di-Hydrogen + 2 C.C. -> 4 Faecium

Infinite Faecium:
Use this once in a while to make more Faecium without Di-Hydrogen to keep your Carbon-Production going:
3 Faecium -> 2 Mordite (+ 2 C.C. -> 8 Faecium)

Yield: 3 Faecium (+ 2 C.C.) -> 8 Faecium

Overall Yield:
3 Faecium + 6 C.C. -> 8 Faecium + 4 C.C. -> 4 Faecium + 12 C.C.
=> 6 C.C. -> 12 C.C., 3 Faecium -> 4 Faecium

Infinite Sodium:

1 Sodium + 1 C.C. -> 2 Sodium Nitrate
1 Sodium Nitrate -> 2 Sodium

Yield: 1 Sodium (+ 1 C.C.) -> 4 Sodium

Infinite Pure / Magnetised Ferrite / Ferrite Dust:

1 Pure Ferrite + 1 C.C. -> 3 Magnetised Ferrite
1 Magnetised Ferrite -> 2 Pure Ferrite

Yield: 1 Pure Ferrite (+ 1 C.C.) -> 6 Pure Ferrite / 1 Mag. Ferrite (+2 C.C.) -> 6 Mag. Ferrite

Infinite Ferrite Dust:
1 Dioxite (s. Elements, 1 Sodium Nitrate + 1 C.C. -> 2 Dioxite) -> 1 Ferrite Dust.
Yield: 1 Sodium Nitrate + 1 C.C. -> 2 Ferrite Dust

You can also make Ferrite Dust out of Pure Ferrite with Oxygen, if you have a lot of that:
1 Pure Ferrite + 1 Oxygen -> 2 Rusted Metal
1 Rusted Metal -> 2 Ferrite Dust (kinda slow)
Yield: 1 Pure Ferrite (+ 1 Oxygen) -> 4 Ferrite Dust

1 Mordite + 1 Sodium Nitrate -> 4 Marrow Bulb (This can also be harvested in caves, but refining is gonna be a lot quicker if you need large amounts)
1 Marrow Bulb + 1 Cobalt -> 2 Ionised Cobalt
1 Ionised Cobalt -> 2 Cobalt
Yield: 1 Mordite + 1 Sodium Nitrate -> 4 Ionised Cobalt / 8 Cobalt (if you have 1 to start the loop)

Infinite Salt / Chlorine
This requires Oxygen which can’t be made infinitely (although it can be produced with the help of Nitrogen), but if you have that readily available, this is where you wanna use it. It is imho easier to make money with Cobalt, though, especially if you don’t mind exploiting the game by market-crashing.
Resources needed: Medium Refiner, Di-Hydrogen / Salt / Chlorine, Oxygen

1 Di-Hydrogen + 1 Oxygen -> 1 Salt
2 Salt + 2 Oxygen -> 5 Chlorine
1 Chlorine + 2 Oxygen -> 6 Chlorine

1 Sodium Nitrate + 1 C.C. -> 2 Dioxite
2 Dioxite +1 Pure Ferrite / Ferrite Dust -> 1 Phosphorus
2 Phosphorus +1 Pure Ferrite / Ferrite Dust -> 1 Uranium
2 Uranium +1 Pure Ferrite / Ferrite Dust -> 1 Pyrite
2 Pyrite +1 Pure Ferrite / Ferrite Dust -> 1 Paraffinium
2 Paraffinium +1 Pure Ferrite / Ferrite Dust -> 1 Ammonia
2 Ammonia +1 Pure Ferrite / Ferrite Dust -> 1 Dioxite

If you have Gold available or the recipe(s) to make it easily, you can turn that into Pyrite:
1 Gold -> 1 Pyrite or
1 Gold + 1 Oxygen -> 2 Pyrite

Since Dioxite is so easy to make (both Carbon and Sodium can be infinitely made), I would usually start from there, but if you have one of the other elements readily available, you can of course start anywhere in this loop.

Resources needed:
1 Ammonia = 2 Paraffinium + 1 Pure Ferrite = 4 Pyrite + 3 PF = 8 Uranium + 7 PF = 16 Phosphorus + 15 PF = 32 Dioxite + 31 PF = 16 Sodium Nitrate + 16 C.C. + 31 PF
1 Paraffinium = 2 Pyrite + 1 PF = 4 Uranium + 3 PF = 8 Phosphorus + 7 PF = 16 Dioxite + 15 PF = 8 S.N. + 8 C.C. + 15 PF
1 Pyrite = 2 Uranium + 1 PF = 4 Phosphorus + 3 PF = 8 Dioxite + 7 PF = 4 S.N. + 4 C.C. + 7 PF
1 Uranium = 2 Phosphorus + 1 PF = 4 Dioxite + 3 PF = 2 S.N. + 2 C.C. + 3 PF
1 Phosphorus = 2 Dioxite + 1 PF = 1 S.N. + 1 C.C. + 1 PF

Copper, Cadmium, Emeril, Indium, Chromatic Metal

To get an infinite Loop with those, you need some Emeril or Indium to start with. Indium is more effective, but Emeril works as well.
Careful not to run out of the base material, never convert everything into Chromatic Metal !!!

Infinite Indium:
Resources needed: 3 Indium (you always need 1 more to start converting the CM back into the base material)
2 Indium -> 4 CM
1 Indium + 1 CM -> 2 Indium

Yield: 1 Indium -> 2 Indium

Infinite Emeril:
Resources needed: 3 Emeril
2 Emeril -> 3 CM
1 Emeril + 1 CM -> 2 Emeril

Yield: 3 Emeril -> 4 Emeril

Infinite Chromatic Metal:
Use either of the above methods and use spare Emeril or Indium to make Chromatic Metal:
2 Indium -> 4 CM / 2 Emeril -> 3 CM
Indium is more effective.
You can also use the following method, if you have Gold and Silver available or the recipes to make them easily, but otherwise Gold + Silver are too complicated to make (see below) to make this worthwile:
1 Gold + 1 Silver + 1 of either Copper, Cadmium, Emeril or Indium

You can also use the activated variants of Copper, Cadmium, Emeril or Indium to make CM, but this only works to get Chromatic Metal, you can’t turn CM back into activated metals, so there is no possible infinite with them.

Infinite Copper and Cadmium:
To create infinite amounts of these, it’s easiest to use either Indium or Emeril to make infinite amounts of Chromatic Metal, then you can use that to create Copper or Cadmium:
1 Copper + 1 CM -> 2 Copper
1 Cadmium + 1 CM -> 2 Cadmium

You can also use the following method for Cadmium to start out, but it is worth it to unlock Emeril and/or Indium quickly, since those are way easier to duplicate.

1 Pure Ferrite + 1 Cadmium -> 2 CM
1 Cadmium + 1 CM -> 2 Cadmium
(Note: You can also get started on Cadmium by buying a Pulse Engine Module (->75 Cadmium + 75 Deuterium) or ship weapon Module (->125 Cadmium + 75 Silver), installing it and destroying it, which will give you some Cadmium to start the loop)

Yield: 2 Cadmium -> 3 Cadmium

Note: You can use Pure Ferrite to duplicate Emeril and Indium as well (Pure Ferrite + Emeril = 3 CM, Pure Ferrite + Indium = 4 CM), but the above described method is a lot easier, so I recommend that one.
Note that if you put in Copper instead, it just uses up Pure Ferrite without actually increasing the amount of Copper (1 Pure Ferrite + 1 Copper -> 1 CM).

Infinite Gold:
Note: it’s a lot easier to make Lemmium/Granite/Magno Gold in your inventory at the cost of more base materials, if you have the recipes for them.
Resources needed: Large Refiner, 10 Gold OR 20 Silver, Cobalt/Pure Ferrite, Dioxide/Uranium/Phosphorus/ C.C. + Sodium Nitrate (to make Dioxide)
I am not mentioning some methods to make Gold, where one of the required components can’t be made infinitely. Pure Ferrite can also be replaced by double the amount of Ferrite Dust, but Pure Ferrite is easier to make imho.
You can also use 5 Platinum or 20 Tritium instead of Silver or Gold, but those are harder to come by.

30 Uranium + 60 Pure Ferrite + 10 Gold OR 20 Silver -> Lemmium
30 Phosphorus + 30 Ionised Cobalt OR 60 Cobalt + 10 Gold OR 20 Silver -> Magno Gold
30 Dioxide + 30 Ionised Cobalt OR 60 Cobalt + 10 Gold OR 20 Silver -> Grantine

Magno Gold / Lemmium / Grantine -> 125 Gold
With the right recipe, you can also make those without a refiner, but this requires a lot more Ferrite or Cobalt, so I prefer using the refiner.

If you have Oxygen readily available:
1 Ferrite Dust + 1 Oxygen + 1 Emeril = 10 Gold

Infinite Silver:
Note: it’s a lot easier to make Aronium/Herox/Dirty Bronze in your inventory at the cost of more base materials, if you have the recipes for them
Resources needed: Large Refiner, 10 Gold OR 20 Silver, Cobalt/Pure Ferrite, Paraffinium/Pyrite/Ammonia or resources to make those (see section Elements)
You can also use 5 Platinum or 20 Tritium instead of Silver or Gold, but those are harder to come by. Pure Ferrite can be replaced by double the amount of Ferrite Dust.

30 Paraffinium + 30 Ionised Cobalt OR 60 Cobalt + 10 Gold OR 20 Silver -> Aronium
30 Pyrite + 60 Pure Ferrite + 10 Gold OR 20 Silver -> Dirty Bronze
30 Ammonia + 30 Ionised Cobalt OR 60 Cobalt + 10 Gold OR 20 Silver -> Herox

Aronium / Dirty Bronze / Herox -> 250 Silver
With the right recipe, you can also make those without a refiner, but this requires a lot more Ferrite or Cobalt, so I prefer using the refiner.

Infinite Platinum:
1 Silver + 1 Gold -> 1 Platinum

If you have Oxygen readily available (can’t be duped):
1 Ferrite Dust + 1 Oxygen + 250 Chromatic Metal -> 10 Platinum

You can also refine Geodesite or Iridesite into 250 Platinum:

Geodesite = 1 Dirty Bronze + 1 Herox + 1 Lemmium (= 500 Silver + 125 Gold -> 250 Platinum)
This requires half the amount of Gold, but double the amount of Silver that you would need otherwise, so if you have Silver readily available, but have to make Gold, this is a decent alternative.

Iridesite = 1 Aronium + 1 Magno-Gold + 1 Grantine (= 250 Silver + 250 Gold -> 250 Platinum)
This requires the same amount of resources as combining Gold and Silver.

Nitrogen, Sulphurine, Radon:

1 Nitrogen + 1 Chromatic Metal -> 1 Sulphurine
1 Sulphurine + 1 Chromatic Metal -> 1 Radon
1 Radon + 1 Chromatic Metal -> 1 Nitrogen

For how to make infinite amounts of Chromatic Metal, see the section Metals.

Oxygen:
Salt + Nitrogen -> Kelp Sac
Kelp Sac + Carbon / C.C. -> Oxygen

You are going to need one of the plant to get you started, then you can just make more with the corresponding element.
You can make the plants using Gases, but those can’t be made infinitely, so I would always just make 1 plant to get you started and then use the corresponding element to make more.
I also suggest always keeping at least 1 of each plant around to make more later, since you’ll need them in a lot of crafting recipes.

Frost Crystal
2 Dioxite + 1 Oxygen / 1 Dioxite + 1 Radon -> 1 Frost Crystal
1 Frost Crystal + 1 Dioxite -> 2 Frost Crystal

Solanium
2 Phosphorus + 1 Oxygen / 1 Phosphorus + 1 Sulphurine / 1 Di-Hydrogen + 1 Sulphurine -> 1 Solanium
Solanium + Phosphorus -> 2 Solanium

Cactus Flesh
1 Pyrite + 1 Sulphurine / 2 Pyrite + 1 Oxygen -> 1 Cactus Flesh
1 Cactus Flesh + 1 Pyrite -> 2 Cactus Flesh

Star Bulb
1 Paraffinium + 1 Nitrogen / 2 Paraffinium + 1 Oxygen -> 1 Star Bulb
1 Paraffinium + 1 Star Bulb -> 2 Star Bulb

Fungal Mould
1 Ammonia + 1 Nitrogen / 2 Ammonia + 1 Oxygen -> 1 Fungal Mould
1 Ammonia + 1 Fungal Mould -> 2 Fungal Mould

Gamma Root
1 Uranium + Radon / 2 Uranium + 1 Oxygen -> 1 Gamma Root
1 Uranium + 1 Gamma Root -> 2 Gamma Root

This can be crafted, but since Tritium can only be bought or found in asteroids, it’s gonna be hard to come by. Luckily it’s not needed for many recipes.

Material — Source — Usage

Tritium — Source: Buying, Asteroids — Ship Fuel
Silicate Powder — Source: Terrain Manipulator — Crafting
Cyto-Phosphate — Source: Underwater plants — Rarely used for crafting
Basalt — Source: Volcanic planets — Not used anywhere
Pugneum — Source: Sentinels — Crafting, Refining (can mostly be replaced there)
Activated Copper / Cadmium / Emeril / Indium — can be replaced by their normal counterparts
Residual Goop / Runaway Mould / Living Slime / Viscous Fluids — can be turned into Nanites

Using Refiner:
Platinum x35 → Nanite Cluster x1
Platinum x25 + Gold x15 + Silver x15 -> Nanite Cluster x1 (This is more expensive, essentially 40 Platinum for 1 Nanite Cluster, but if you have Gold or Silver lying around, you might wanna choose this to save time)

Time needed:
When using this method, this would only net you 0,96 Nanites/minute (pure refiner time), if you only used one refiner (large refiner needed to make gold and silver, everything else can be done in a medium refiner), however using several refiners speeds things up considerably, so I would recommend using all possible 3 medium and 2 large refiners, if you choose to use this method. Having Silver (or Pyrite, Paraffinium or Ammonia to make it) readily available will speed this up considerably, since the most time is spent on making Silver, Gold can be made pretty quickly even from scratch.

Although not craftable, but easily findable/buyable, you can also turn any of the following into Nanites with your refiner, but it’s taking very long to do, so not really worth grinding imho:
Residual Goop x5 -> Viscous Fluids x5 -> Living Slime x5 -> Runaway Mould x5 -> 1 Nanite Cluster

Using Nutrient Processor:
2 Mordite (see above on how to make infinite amounts) -> 2 Meat Flakes -> 2 Meaty Chunks (put in 2 slots) -> Mystery Meat Stew
50 Mordite in 5:12 Minutes (pure processing time) for 25 Mystery Meat Stew

To turn this into Nanites, you have to bring it to Cronus on the Space Anomaly and sell the Stew one by one. The amount of Nanites you get is random. I got on average 68.175 Nanites per Stew on a sample size of 400 Stew (27270 overall).
Time to turn in 25: about 2:25 minutes (when standing in front of Cronus (me on my PC))
-> overall ‘production- + turn-in-time’ 1704.4 Nanites in 7:37 minutes (per 25 Stew) + time to get to Cronus
-> 68 Nanites per 18.28 seconds (per Stew) + time to get to Cronus

This should be the fastest way to make Mystery Meat Stew, which seems to be the easiest way to make nanites with cooking and I think the only to make Nanites from scratch. There are other ways to make the Stew, but it doesn’t seem to make a difference what you use in terms of Nanites you get. I tested 2 ways and both gave me about the same amount of Nanites. Let me know if you have different information about any of this.

Since you have to go to the Space Anomaly to turn this in, using Platinum is probably a bit faster, if you have some of the needed elements/Silver available, but it is more complicated to make (depending on where you start). However, using the Nutrient Processor, you have to turn in every single Stew one after each other, so this can get very annoying, so choose whichever method you prefer. 😉
Of course there are a lot of other methods to make nanites out there and a lot of them are probably gonna be quite a bit faster than either of these.

Other (non-infinite/crafting) ways of making Nanites + down-/upsides:
Note: This is in no way a complete list, I’m just listing what I think are (some of) the most effective methods.

1) At the release of Sentinel-update (Feb 2022), the best non-exploitive way is probably hunting sentinels at around 35-45.000 Nanites per hour. The better your weapon the faster, so you’re going to need a decent weapon for this. You also need a decent amount of inventory space for this.
Thanks to sstooney in the comments and Xaine(‘s World) for providing a video:
Xaine-Video
Note: You can safely do this from inside a building even with your starter weapon by letting the situation calm down every time before more dangerous sentinels appear, but that’s probably a pretty slow method.
Edit 04/22: I haven’t tested this myself, but apparently this got nerfed into the ground. Feel free to let me know your experience with this.

2) Make a farm to produce Nanites: fastest should be Fungal Mould (Fungal Mould -> Non-Toxic Mushroom -> x2 -> Fibrous Stew) or Gamma Root (Gamma Root -> Sievert Beans -> x2 -> Fibrous Stew). Both of those should provide the same amount of Nanites per plant, so take what you can get your hands on easier. Both take one less step in the Processor than above mentioned method using Mordite, but Mordite is a lot easier to make infinite amounts of, if you don’t use farming, which is why I used that one above.
If you’re on PC and are willing to make a script to turn in food to Cronus while being AFK, this might still be the most effective (non-exploitative) method, but you still need a decent amount of inventory space and a good setup to do this effectively. Turning stuff in to Cronus one by one is a huge ****, though, if you do it manually.

3) Buy S-Class ships, scrap them and sell the resources for Nanites.
This gives decent amounts of Nanites without completely ruining your mouse/controller, but it’s very expensive to do.

4) (exploitative) Runaway Mould farming Xaine-Video
You need to get lucky finding a Runaway Mould-deposit and need to build a base to farm them. This is not generally exploitative, but if you want to do this effectively, you have to exploit it by moving away from it at least 600u and come back to make them respawn.
If you don’t mind this, this should easily still be the most effective method to get Nanites, apart from editing your save file. 😉

5) (only really effective by exploiting) buy Platinum / Runaway Mould (or Residual Goop / Viscous Fluids / Living Slime, but those take a lot long time to refine and I’m not sure you can buy all of them, I think I’ve only seen Residual Goop and Runaway Mould) and turn that into Nanites with your refiner.
This is either going to cost you a lot of money or you’re going to have to exploit the game by market-crashing to buy the resources for free.

Let me know if you know any faster methods to make Nanites by crafting/cooking (or share your other favourite methods in the comments, if you want 😉 )

Thank you for everyone posting comments about this, I’m reading all of them. I might not respond to everything, if I don’t really have anything to say, but I appreciate all of them (as long as they’re friendly). 😉