How do I record my rap?

On the basic end, you could use a tape recorder.  A step up would be using a digital voice recorder, though they cost a little more.  Digital voice recorders have the added advantage of being able to send audio straight to a computer, where it can be edited and put on a CD or made into an mp3.

If you have a computer nearby, you can use a program like Audacity to record the audio.  If you go this route, you'll need to get a USB audio adapter to be able to hook up the mics to your computer.

Once it's recorded, is it really freestyle anymore?

Hee hee.  Good point-- not technically.  But recording your freestyles can help you freestyle much better.  

Can I hear some of the stuff you guys have done?

As soon as we record some, sure!