Set up Audacity to record your vocals. This is as simple as creating a new project and setting up a track to record the microphone.
Do a quick test recording. Listen to the recording to detect any background noise or buzzing.
Check the cables and microphone to fix any buzzing noise. Use headphones during the recording to prevent any feedback. If you can't get a clean recording, try a different microphone or cables until you eliminate the buzzing.
Move to a quieter space if there is any background noise. It is much easier to create a clear recording from the outset than to use the tools in Audacity to clean it up after the fact.
Record the rap. You may have to enunciate more than you would for a live performance to capture understandable lyrics. When recording, you have the option of doing as many takes as you need to get it right. Don't settle for vocal gaffs.
Use the reverberation and equalization tools to improve the sound quality of the recording after the fact.These tools allow you to tweak many facets of the recording. Experiment until you are happy with the sound quality.