How do you make karaoke songs with Audacity?

Ah. There is no hard and fast rule for this; in fact, most of the time it can't be done, and it is simpler to make a backing track from scratch. However, you might be able to come close-enough to what you want, depending on your audio file.

If the instrumental music differs in each ear, but the vocals are evenly panned ("center-panned"), you can split your stereo track to mono by using "Split Track," then "Invert"ing one of the tracks, and finally sticking them back together with the good old "Make Stereo Track."
There is a plugin (at least for Linux Audacity) called something along the lines of, "Remove Center-Panned Vocals."
Both of these methods will leave you with a soft, tinny remainder of the singing (usually), like the shadow left when you erase the number fifty-eight off of your math homework. If none of the instruments are center-panned, and the vocal tracks all are, this should work great, perfectly, even. Otherwise, you'll get the leftover vocals, plus any center-panned instruments will be similarly crappily removed.

If you make use of the "Equalizer," you may be able to eliminate most of the vocal out of your track.
Using "Amplify" to decrease the maximum amplitude may allow you to make whatever is left of the vocals quiet enough that nobody will notice.
You might try the "Bass Boost," depending on what kind of music it is. If you can remove the vocals most of the way, and the song has a heavy beat, chances are that if you just up the bass, it will cover up the remainder.

If you for some reason have an acapella track of the song, and it is identical to the vocals in the song you want the instrumental of, you can:

Line up the two tracks Exactly (if they aren't matched exactly, it won't work), then "Invert" one of them. They should also be the same volume (the vocals in the song and the acapella track), because if one is louder than the other, you will hear the vocals as loud as the difference of the volumes of the two tracks.

If you have a poor quality version of your song (as in, played, re-recorded via analog device, then converted to digital), you won't be able to remove center-panned vocals (Using the "Equalizer" will still work).

Sorry, man, a dilemma we all have, and right now, there is no easy answer.