Audacity is a great open source audio editor program, available for Windows and Macintosh http://audacity.sourceforge.net/
Here are some learning resources for it
Audacity Tutorials
http://audacity.sourceforge.net/manual-1.2/tutorials.html
Wiki
http://wiki.audacityteam.org/wiki/Category:Tutorial
Removing vocals with Audacity http://wiki.audacityteam.org/index.php?title=Vocal_Removal
Mixing two songs together http://www.ehow.com/how_5061510_mix-songs-audacity.html
Pingback: Q. Is there free software for recording and mixing music? | CanadaRAM: Memory and Computer Q&A