I want to transform a music DVD (shows from my favorite bands) into a
CD, so I can listen to the show in my CD player or my iPod. Is it
possible? Is there a specific software to do this transformation? How
does it work? I work with a PC, and use the Windows XP.

Yes it is possible.  You will need a software tool.  Mac users use
Handbreak, Mac the Ripper and a few others.  You could also play the
DVD on a DVD player and connect it to a realtime CD Audio Recorder. 
All you would need to do is hook up the audio to the CD recorder and
there you go.

you can got to this site:
http://www.mymusictools.com/download/video-enhancement/ . it has all
the software you will ever need to do what you want. on the first page
there are 2 programs that i have tried and they work extremely well.
hope this answers your qusetion

You need a DVD audio ripper.
Best I found was from ImToo.
You can download from: http://www.imtoo.com/dvd-audio-ripper.html
This will extract the sound track on any DVD into MP3 files which you
can then burn to CD with appropriate software (NERO:
http://www.nero.com) or load to your ipod in the normal way.