This is my guide for fishless cycling using the ghostfeeding method (i.e. using fish food).
Ammonia - the product of fish waste, decomposition, and just general ammonification. Toxic to both freshwater and marine fish.
Ammonification - conversion of organic nitrogen into ammonium (ammonia). This is really as much as you need to know.
Microorganism - small living things. Include bacteria, but also other living beings, such as algae, fungi, and so on. There is some debate amongst scientists about what can exactly be classified as a microorganism. Mostly irrelevant to the aquarium-keeping hobby, so don't worry too much about it.
Nitrification - The process in which ammonia is oxidized to nitrite then nitrate. Do not worry about what 'oxidized' means, you can use the term 'converted' instead. Not exactly important, but may be of interest: ammonia can actually be directly converted to nitrate, by microorganisms such as Nitrospira inopinata.
Nitrifier - A microorganism that either converts ammonia to nitrite, or nitrite to nitrate (or ammonia to nitrate directly, see nitrification). Common genera ('groups') of nitrifiers are Nitrosomonas, Nitrosospira, and Nitrospira. In marine environments, certain nitrifying Thermoproteota species are also common, specifically from the genera Nitrosopumilus and Nitrososphaera.
Nitrate - The final product of nitrification. Nitrate can be consumed by certain organisms, including microorganisms in anaerobic processes, or by plants and algae. Nitrate toxicity varies greatly depending on live stock species, but generally not as much as ammonia or nitrite.
Nitrite - The product of ammonia oxidation, which is then oxidized to nitrate. Nitrite is very toxic to freshwater fish, but needs to be at very high concentrations to be toxic to marine fish. Toxicity varies between marine fish species, but probably around 100+ppm is enough to be lethal for some species, and higher for others. I would suggest nonetheless keeping nitrite below 25ppm for marine systems, as even if not lethal, higher concentrations of nitrite can still cause disease.
Here are the steps to follow:
Add as much food and as often as if the tank was fully stocked. This is called 'ghostfeeding'. So if you are going to say have a betta in a ten gallon and will feed it three pellets a day, then add three pellets a day to your tank.
Do water changes if ammonia and/or nitrite gets too high. If you want to know more on when to do a water change, see here.
Once you are able to ghostfeed for ten or so days straight without a water change, and ammonia and nitrite remain zero during that time, then you can consider your tank 'cycled'.
That's it. I don't recommend this method though. There are a few reasons.
It may not be accurate. One may think one'd feed the tank three pellets a day, but turns out the fish will need six, then well, that's no fun. Of course you can always just double the amount of food or whatever you ghostfeed just to be sure, though of course that may mean the cycling process will take longer.
You may not be growing nitrifiers. You may end up growing non-nitrifying heterotrophs, which are microorganisms (bacteria and other organisms) that consume ammonia not via nitrification, while also growing very well using organic substrates, which would be plenty in fish food. Relying on these to keep ammonia in check may not be a great choice, but still, some people consider a tank 'cycled' nonetheless, as per defined here. I don't though, hence why I put 'cycled' in quotation marks here.
It may require more effort. Adding fish food may result in ammonia spiking far too high and may stall the cycle and require a water change.
It may nonetheless not cycle your tank even with an amended definition as per above. The problem is that my 'ten days' is only an estimation, as fish food can take longer to decompose under different conditions... that are too many to list or even account for at times. To be safer, I would recommend a month or so of ghostfeeding, but who'd want to wait a month?
So yeah. While this method is 'simpler' than say ammonia-dosing, I would not recommend it. Fishless cycling by ammonia-dosing is the superior method compared to all other cycling methods, and thus I'd suggest doing it if possible.