You need to prepare the lyrics and music before you can even think about recording an album. Some artists prefer to write the lyrics before incorporating them with beats, while others like to write their lyrics with the beats already prepared and providing a rhythmic structure. Acquiring beats can come from a variety of sources: collaborating with a producer, buying beats off other established producers or composing your own beats.
Plug in your microphone and fire up your recording software. Pro Tools is generally considered to be the premier program for recording rap songs, but other programs like Reason and Logic will do the job as well. If you're a novice to recording music through software, it might be easier to work with more basic software like GarageBand for the Mac or Acid for the PC.
Streamline your production to fit the way you want to rap. There are many ways to ride a beat, but the beat stays on its progression and will not ride with you. The only way to solve that is to change and tweak the beat to fit your needs. Fiddle with the tempo and pitch to find what's right for your rapping style.
Start rapping into the microphone. Don't be afraid to use 10 or 12 takes to record a full song. Even seasoned rappers are prone to slip up and fumble while recording. Rap requires concentration and patience and it demands perfection. It is the type of music where flaws in recitation can be pointed out easily. It's easier to ensure the quality of your recording if you can find a way to soundproof your studio, but it's not completely necessary.
Start the process of mixing the lyrics with the music. This is where the caliber of the recording software comes into play. The more complex it is, the more it will be able to assimilate the vocals with the music. Pitch, tone, tempo and volume are all critical elements of a song. Make sure that everything matches up to your liking. Mixing in itself is a science, so don't be discouraged if you can't do it on the first try.