Biting is one of those innate things that cats like to do, especially as kittens. Instinctively, cats want to play fight with things, which hones their hunting skills for later in life. Of course, house cats don't have to hunt anything other than the food bowl, but the instinct is still there.

With a new cat, it's important to never let it use your hands as toys to play fight with. This would teach them that it's okay to bite and claw at your hands, which will stick with them and be very hard to discourage.

Next time your cat tries to bite you, firmly say, "NO" and don't interact with it. If you just say "no" and keep letting it bite you or keep playing with it, it won't understand what you mean.

If that doesn't work, move up to making loud noise. Clap your hands together, or hit a table or wall. Don't hit the cat, because that would only make it fear you. The noise will startle the cat and very quickly it will learn that biting illicits a bad response.

Repetition is critical for cats to understand what you want. You can't talk to your cat, so there's no other way to communicate to it that you don't want it to bite you any more. You should also do the same thing (saying no, clapping your hands, etc.) if the cat tries to bite other people, to further reinforce that biting people is a bad thing.

Most cats shouldn't take too long to learn that biting is bad. Particularly stubborn cats (like mine!) can take a few weeks, but they eventually learn and stop doing it, leaving your hands and house guests much happier.