Work on your skills. Just because you're a rapper doesn't mean you'll be able to compete in a rap battle. You need to work on coming up with rhymes off the top of your head, without writing them down and memorizing them. You can do this by rhyming about various objects you see or people you know. This is called "freestyling."
Find a battle in which to compete. There might be one at local college or night club, or sometimes one will simply transpire on the street. Organized battles are run a bit differently than those that take place on the street, but either way you'll have to bring your best game.
If you are chosen to rap first, quickly observe your opponent and choose rhymes that are appropriate for him. These rhymes should be based on his appearance, behavior, clothing and any other characteristics you think could be exploited. For example, if your opponent is wearing very tight clothes, you might want to make fun of him for that.
If you are going second, you should follow the instructions described in Step 3, but also use your opponent's rhymes against him. In other words, if he makes fun of you for your shoes, you could acknowledge your shoes aren't the best, but respond with something about his appearance that is even more embarrassing.
Try not to be nervous or get too angry. You want to keep your composure and keep the crowd on your side. Remember, in most battles the crowd determines the winner so you want to be as clever and creative as possible with your rhymes. This is the best way to win over the crowd.