This article is from the CD-Recordable FAQ, by Andy McFadden (email@example.com) with numerous contributions by others.
If you have a stand-alone audio CD recorder, this should be straightforward.
Either you have a microphone input or you don't.
On a computer, you probably don't want to do this. The greatest advantage
of using a computer-attached recorder is that you can edit the result
before recording it. CD-R is write-once media, so if you make a mistake,
you can't fix it later.
If you're determined to do this, Roxio's Spin Doctor (part of Easy CD
Creator) can do what you want. Connect the microphone to the input on
the PC sound card, start up the software, and record when ready.
The situation on non-PC platforms is similar: you can do it if your
software supports it.