Cats can be found anywhere.
If you would like to tame a Cat then you have to have cooked fish.. You have to eject the cooked fish at the cat you want to tame; when the cat eats the fish (the fish will disappear and you will hear a nom-ing sound). A box that asks what you would like to name your Kitty will appear. If said box does not appear, you can name your cat by using a Medallion.
Kitty will not follow you. To have kitty move, you must manually right click the kitty (with an empty hand) to pick the Cat up. If you would like a cat that follows you then a Ocelot might be the thing for you. To get kitty off your shoulders right click and kitty will jump off.
If a food bowl appears above the kitty's head, it means they are hungry. Fill their food bowl (kitty bed) by right clicking with pet food.
If a litter box appears, make sure they have a clean litter box because, well, they need to go... "..." means don't bother them.
A tree means that they want to be outside, but providing a sapling will make them happy.
This means that your kitty is using its litter box at the moment.
If the kitten keeps attacking you, they want to play. Create a ball of yarn, and right click on them with it! Kitty will play until satisfied, and you can reclaim it by walking over the item. They can be used countless times.
Taking care of KittyEdit
Feed two different cats Cake. You have to wait for 1/2 a real day for the new kitten. Mating is much like any other breedable mob.