Quick checklist of things, most important first.
- Is cat pooping and peeing in the litterbox? He should be pooping about twice a day, and peeing at *least *twice a day. Check said poop and pee. Does the poo have any segments of worms (look like short white/grey threads) or blood or really black tarry-looking spots, or is the poo extremely light (think tan or yellow) and liquid? Is his pee either brown or bloody? If yes to any of those - off to the vet pronto.
If not, then his internals are going mostly ok for the immediate future. Don’t keep just feeding him wet stuff - do give him cans of wet food (try a can each morning and evening) but also leave a bowl of dry food and a bowl of water out for cat to eat at will. Cats (usually) will not stuff themselves sick like most dogs do. Remember to check and replace the water every day - cat is most likely dehydrated. If you can remember, keep track of how much dry food the cat is putting away each day, and make a record of it - vet will want to know.
- Check his face.
Look closely at his eyes - are they weeping puss or slime? If so, off to vet pronto!
Look at his mouth if he will let you - does he have missing/rotted teeth or sores? If so, off to vet pronto!
Check his ears - are they black and tarry on the insides? If so, off to vet pronto!
Check his nose and mouth - is he snotting or drooling constantly? (don’t count drool when purring/being petted - lots of cats get drooly when they’re being loved on) If so, off to vet pronto!
Check his second eyelid and his gumlines. If his second eyelids are not retracting fully, he could be slightly ill, or more likely dehydrated. If his gums are very light or totally white, he is most definately dehydrated. If you see *both *of these, off to vet pronto!
If none of the above applies, then his intake systems are doing good. Keep feeding regular, and try to get him to drink broth or tuna-water if he’s willing.
Check his walking and sitting - does he limp? Off to vet! Does he favor one leg or walk crooked? Off to vet! Does he sit strangely or seem to avoid putting pressure on a particular side or body part? Off to vet!
Check for bodily injury and skin condition. You have to check closely for this - cats are really good/bad about hiding their injuries. In addition to watching him move around (see if he licks any particular place more than others), run your hands along his fur backwards to the grain (do this only a little at a time - cats are generally not fond of the experience) and see if you note lots of fleas and flea poo, or sores/abcesses, or old scars or patchy fur.
These don’t necessarily mean a vet trip unless they are on the head or genitals, or on the feet, or really big or infected/nasty. If fleas, then cat needs a flea bath eventually (as in, he can gain some weight first and then suffer the flea bath later), if small sores, keep an eye on them and head off to the vet if they get bigger or infected, or if cat starts worrying at them constantly.
If none of that applies, then love, feed, water, and keep an eye out on various body functions, and watch him plump out under all the attention! Even if he looks fairly healthy, I would advise going to the vet with him no longer than a month from now - make sure he’s got no diseases or unnoticed worms and start him on his vaccinations and rabies shots.
If you’re keeping him, then you’ll have a lovely cat who will be very happy that you fed and loved him, and if you are not keeping him, the foster/adoption people will be eternally grateful that you gave them a proper pretty and healthy cat to adopt out instead of an emaciated scarecrow that is unadoptable without extensive fosterage and vet work.