The way to do this is by removing audio that's common to both left and right channels, as almost all songs with vocals have the lead vocal panned hard center. 

Check out this link: http://wiki.audacityteam.org/index.php?title=Vocal_Removal.

And if you don't feel like installing any plugins, but will put up with bad sound quality, watch this video: http://www.videojug.com/webvideo/how-to-remove-vocals-to-create-your-own-karaoke-songs-using-audacity

---

Remember, removing vocals causes artifacts in your audio, and generally makes your track smell like hot garbage.  Use this only if you want to jam and you're willing to put up with this sort of quality.  If you're doing a cover track this way PLEASE don't because it will sound horrible.  Try looking for isolated audio tracks on Youtube instead to play along with if you're recording a cover.  Check this one out: http://www.youtube.com/watch?v=l95YNpTlrZY