When you get a new kitten it can be an exciting time, but you also may not know exactly what to do with a new kitten. How often should I feed him? What should I feed him? When should I take him to the vet? Etc. Well, you should know how old your kitten is (if not, bring him to the vet to get an estimate). If he is younger than four weeks, he should only be eating mother's milk or milk replacement (not cow's milk). If he is between four and eight weeks, you should be in the process of weaning onto kitten food. After eight weeks, he will only be on kitten food.
The best case for a baby kitten is to have its mother give it milk when it needs it and for you to leave it be. However, this is not always possible. You may not know where the mother is, or the mother may be refusing to feed one kitten. In these cases, you should be giving the kitten milk replacement. You can get this online or at a pet store. It will come in either a liquid form or a powder which you will have to mix with water. You will want to give the formula to the kitten via a needle-less syringe or a small dropper. Make sure that the flow of milk is slow, you may suffocate them if there is too much milk flow.
Make sure you choose a high quality kitten food. Get a recommendation from your vet if you like. It should be made almost entirely from meat, as that is a cat's natural diet. Only feed it kitten food, not cat food. Kitten food is more calorically dense, so it helps the kitten grow and expend all of the energy it requires.
Whereas an adult cat can be fed once or twice a day, a kitten needs to be fed about four to five times a day. This is because of the calorie requirement a kitten needs. They will not be able to eat enough in one sitting. And, if they do, they will likely suffer from 'scarf and barf', where a cat eats too much food too fast and proceeds to vomit it all up.
I hope that this article has answered all of your questions about feeding kittens at any point of their life cycle. Have fun with your baby kittens!