First you look around and try to find a cat. Cat mobs come in many colors, so you have a lot to choose from. A place where cat mobs commonly spawn is a village, no matter what biome it’s in. Ocelots can be found in the jungle biome, but you can’t tame them.
Once you find a cat you like, grab some raw fish. Right click the cat (or get close to the cat and press the tame button at the bottom of your screen) until you see hearts surrounding your cat. The cat will have a nice red collar on, and be sitting on the ground. If you want your cat to stand, right click it again without the fish, (or get close to it and press the stand button) and your cat will now stand up and run to follow you. If you have an ocelot or don’t want your cat to follow you but still wander, hold raw salmon and slowly approach the cat. Then, slowly walk back to you base, and the cat/ocelot will follow you home.
If you want to change the color of your cat’s collar, hold a dye and right click the cat (or get close to it and press the dye button) and your cat’s collar will change to the color of the dye.
Don’t leave an untamed cat next to chickens or parrots, because your cat will eat them!
Breed two cats by right clicking them both while holding raw fish when they are close to each other (or by getting close to both and pressing the feed button at the bottom of your screen) but make sure your cats are in full health, or they will not enter breeding mode.