Learn about the ensemble holding the audition. Determine the style of music and what role you will perform. For example, a group that hires Broadway singers will want to hear music from Broadway.
Assess your range and capabilities. The song you select is one of the few parts of an audition you have control over. Select a song that shows off your range and capabilities in a flattering way. Don't choose a technical piece if you sing best with lyrical songs. If you have a high range, select a piece that demonstrates that range.
Prepare a song you can sing from memory. Memorize the song well in advance to prevent the possibility of forgetting your words in the middle of the piece. If you have trouble memorizing songs, don't pick a song that is overly complicated. Select a piece that has repetitive phrases to minimize the amount of memorization you must complete.
Select a song that is difficult enough for you to show off your expertise and minimize any weaknesses, but not so difficult that you are prone to making a mistake in the audition. Remember that the judges expect you to have this piece well rehearsed. If you have a song that shows off your high range, but exposes a weaker low range, consider another song.