Is it based on the size of the pot? or the size of the plant? or both maybe? How much? -- pretty much, yes.
the pot size and ingredients of your substrate will determine how much water it can hold. how frequently you irrigate is based on how fast the plant can drink some minimum portion along with whatever evaporation occurs. This is why it's good to have the plant properly sized to its pot.
How much? as much as it takes. don't try to chose the volume. Simply water until the entire substrate is wet - a little runoff is fine, and if in soilless context, 10% runoff religiously. In soil you don't want to leech off your pre-amended nutes. a little runoff ensures you avoid re-ocurring dry pockets or zones in the subsrate where minerals can build up where it ebbs and flows but never clears it out before it dries again (minerals remain but plant cannot obtain if dry).
Also, use more than 20% perlite. go closer to 50/50 with soil. It will increase frequency of irrigaiton, but you'll have better roots and better plants. either grow bigger or shave time off your grow at same size, which saves money and your effort.
So, in soil.. water until you get a litle runoff. you can dial it in so that you minimize that leeching of your pre-amended nutes that come in soil. Wait until top 1 " dries and repeat. Feel the weight of the pot. If you water at this point each time it will requie the same mass in water, therefore same volume, roughly (fertilized water is slightly denser). i'd stick to this religiously early. You can probably preempt that a bit in flower, but with 20% perlite stick to 1" drying before irrigating. Seedlings, at this stage i let the top half inch dry or so. when they are sprouts and tap root is not deep, i won't let it dry out quite that much. This only is relevant to 1 irrigation, though. after that the tap root will be all the way down to bottom.
Some soil can last 6-8 weeks before you need to add anything. Fertilize when you see those lower cotyledons start to turn yellow, but start at 1/4 strength. Depending on the concentration you may want that mixed in every other or every third irrigation. personal preferences will come into play. Take notes of how things go and when you applied what fertiliser etc etc. it'll help the next time. and eventually you'll have a good procedure memoried.
You can learn the volume needed retroactively. After you irrigate, pay attention to how much 1 pot takes and repeat at same dry off time. Some plants will drink faster than others. If close enoug convenience comes into play, but in general a wet-dry cycle is healthier for roots and less risky for root disease and a whole assortment of other issues.