Think of what you want your rap lyrics to be about. A relationship? A political or social issue? Life problems? Whatever the case, if you're connected to the message, you'll be more invested in the lyrics.
Learn the structure of rap songs, which often have two or three verses and two or three choruses, in addition to occasional other sections. Listen to songs you enjoy and notice the different parts to help you learn the structure of rap songs
Begin writing lyrics. A line is usually a few words long. Don't worry about whether they're any good; you can edit them later.
Think of rhymes. There are rhyming websites and rhyming dictionaries that can help you find rhymes if you can't think of them yourself. Remember that words don't necessarily have to perfectly rhyme. These are known as "slant rhymes" (e.g., "navy" and "baby").
Try to add multirhymes. These are words that rhyme with more than one syllable in the previous or following phrase (e.g., "Sun set / fun bet"). Many rappers, such as Ludacris, use multi-rhymes. Use slant rhymes with multi-rhymes for your rap song.
Write a hook for the chorus. The hook is the memorable part, the thing that often gets stuck in a listener's head. A chorus is the part of the song that's usually repeated. Thus, a chorus is often fairly simple -- it's often just a few words.
Look over your lyrics. Make changes to lines you don't like. Look for a flow to your words. Look for rhymes and hooks. Continue to make changes until you are happy with the lyrics. It might take some time, but soon you may have lyrics you really like.