Listen to hip hop music. Listen to a lot of it. Having a genuine interest in the genre is the most important aspect in learning to rap and learning to rap well. Avoid filling your mp3 player with only radio hits and seek out more reclusive artists and songs. Peruse the entire spectrum of hip hop artists to find a style that resonates with you. Collect albums deemed classics -- such as Nas's Illmatic -- and listen to them from front to back. What do you notice about these classics? For example, do they deal with similar themes or perhaps have certain traits which make them timeless?
Make friends with other people into hip hop music. Discuss different styles of artists such as Jay-Z, Slug, Rakim and DMX and what makes their style differ from one another.
Talk with amateur rappers in your own circle of friends about their own process of writing, freestyling and recording.
Invest in a notebook. Write down anything that comes to mind. Aim to describe yourself as a person in ways an audience would find interesting. It's forgivable to sound like your influences at this point, and is only natural that you do. Continue to write randomly in your notebook without worrying just yet about creating coherent songs.
Download some instrumentals. Write an entire 16 bar verse to the instrumental. Make sure your chosen rhyme scheme matches the beat by placing your rhyming words on the same beat every measure. For instance, if you rhyme "tainted" on the fourth beat of a measure in standard 4/4 time, then the fourth beat of the following measure will sound more satisfying with a similar rhyme landing on it.
Recite the verse aloud. It probably won't sound the same aloud as it did in your head. Don't fret, this is because you have not yet mastered the vocal delivery for your rhyme. Observe how professional hip hop artists look when they are rapping, pay close attention to the nuances of their facial expressions and breathing.
Recite your own rhyme in front of a mirror an watch your expressions. Ensure your expressions match the message of your words. Chances are if your rapping about a strong or painful but your facial expressions say "bored" then your delivery of the message will conflict with the meaning of your words.
Perform your verse in an as interested, engaged and involved manner toward your subject as possible. Be believable, enthusiastic and energetic. Mute the self-critic in your head and don't worry about making a mistake -- humanity is the key element in rapping and sounding like a pro hip hop singer.