The first step to owning a cat is, well, finding one! If you are particular about certain traits you would like your cat to have, you can pick a breed with those characteristics. If you are not too particular about what kind of cat you own, there are many local adoption centers to check out.
The best idea is to go in person, as many times as you feel is necessary, and to spend time with the cat or kitten. Make sure to pick a cat based on personality. Just because the kitten is adorable, doesn't mean your personalities mesh well. By going in a few times, you should be able to get a cat that is perfect for you.