To feed cats in Minecraft, you need to give them raw salmon or raw cod. To tame a cat, you need to hold the raw fish in your hand and approach a stray cat slowly. Use the raw fish on the cat, and continue to feed it more raw fish until you see red hearts appear all around the cat, which means that the cat is being tamed. Once the taming process is complete, the hearts will disappear, and the cat will become your pet. You can also breed cats by feeding them raw fish while they are in love mode.
Its worth noting that cats do not need any additional items, such as litter boxes or food bowls, and they do not need toys or things to play with. They will follow you around, but you can make them sit by right-clicking on them.