Do you have any specific questions? If you have experience cutting the "old-fashioned" way, then you shouldn't have too much trouble doing it with Audacity. The concept is baaasically the same. I say basically because you have a lot more flexibility to go back and add in more than you did when you were working with tape. To me, the hardest part is always figuring out where I want to cut it.
The way I work with Audacity is roughly this:
1. Import my chosen song
2. Copy roughly the first section I want onto another track. (make sure you add a stereo track if your music is stereo, which most is)
3. Copy other sections I'm considering onto other tracks, sliding them backwards and forward in time, trimming off bits
(Slide - There's a tool with arrows pointing left and right near the cursor button; deleting - highlight section to delete then press delete button)
4. Listen to how transitions sound when played together. I always have a ton of tracks open at a time, and mute ones I don't want to play.
5. Fade out any sections that may need it, if a blunt cut doesn't work.
(highlight the section to fade, then select effects -> Fade Out)
6. While I'm working, I just save as .aup
7. Once I've arrived at something I like, I delete any tracks that contain cuts I ended up not using, then I export to .wav which can then be burned onto a CD.
Hope that helps a bit. It's a bit of an art form, deciding which bits to cut, but that's always been hard! But now, with digital you have the option to go back and try again much more easily