If you would like a cat but you don't know how to get one, this guide is for you.
Your first cat
Finding a cat
Firstly, you should be in, or very close to a jungle biome, as jungles are the only place ocelots spawn. If you are playing on peaceful then none will spawn (the Realistic Minecraft Mod changes that). Be sure to have plenty of raw fish. (at least 10-25 if you want more then 1 cat)
Taming an Ocelot
Wander around the jungle biome until you find an ocelot. Ocelots are a lot like other passive mobs, such as cows and sheep, because they spawn in random areas, even inside leaves. Do not run after ocelots as they will sprint away from you making it hard for you to tame them, and they can not be tamed if placed inside a pit or a pen. Instead, you have to walk slowly towards them (sneaking by holding the Shift is the best way). Do not move the camera suddenly as that will also cause ocelots to sprint away from you (Going into cinematic camera mode by pressing the F8 key may help some players). When you are close enough to the ocelot, stand still while holding a raw fish in your hand, and wait for the ocelot to come slowly come over to you. When the ocelot is five blocks or less away from you, looking at you, and is not moving, keep giving it raw fish by right-clicking the ocelot with the raw fish in your hand, until hearts appear above the ocelot. The ocelot will then become one of three cats, Tabby, Tuxedo, or Siamese.
More cats
Breeding
After you have tamed 2 or more cats successfully, you can begin to breed them if you do not wish to go to the trouble of taming more ocelots.
Keeping them at home
If you do not wish for your cats to follow you around and constantly meow, you can right click them like a dog to make them sit.