You can "rip" (copy) songs from audio CD's with many programs.  You "rip" the songs to the hard drive and then when you have what you want to make a "compilaton" CD, you then create (burn) the Audio CD.  This assumes the CD's you want to copy from are not copy protected CD's.  If they are copy protected, you cannot "rip" songs from them.

MusicMatch Jukebox (some versions) have this capatiblity.  However, there is now a great CD ripping program available (it used to be shareware program), "AudioGrabber".  This program is designed for the exact purpose you want and is fast.  http://www.audiograbber.com-us.net   When "ripping" songs from CD to the hard drive, rip them to a wav format (required for standard audio CD's).  Also use the CD burner as the source drive for ripping, it has a higher "DAE" (digital audio extraction or ripping speed) than a CD or DVD-ROM drive.  Also, with AudioGrabber, or any ripping program, use the "normalization" option so all the songs will have the same volume level.  If you don't normalize and rip songs from various CD's, they will all have different volume levels.

Some hints for burning audio CD's.  Limit your CD-R (do not use CD-RW for audio) burning speed to 12X or lower, this will allow the CD to be compatible with almost all home or car in-dash audio CD players.  If you record it higher it may not play or skip.  Also, if you are going to use it in a car CD player, do not put a paper label on it, just use a magic marker to identify the CD.