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Chances are, you'll be in a classroom or other small room that you've never been in before, with at least one emotionless person staring at you, possibly surrounded by microphones. Try to mentally prepare yourself for this beforehand, and just pretend you're in your band room or bedroom playing for your director or your parents. Most proctors will let you play a few notes to get a feel for the room - simply play your tuning notes, a couple arpeggios, or a short scale. This will also give you a chance to get your bearings and relax. He or she will tell you what to play first - just ignore the robot speech. Often, they'll say something along the lines of "Please play your technical exercise, Rubank Advanced Method, volume two, page 6, exercise 12... please play your technical exercise". In most areas, the people scoring or recording your audition aren't allowed to show any emotion towards you, either positive or negative, during the entire time you are with them. Any positive response might give you false hope or overconfidence, and a negative response would hurt your confidence and cause you to do even more poorly. When you get to the sight-reading (which is usually last), you'll have anywhere from 20 seconds to several minutes to study the piece, depending on how hard it is. Use this time wisely: Finger through it, count it, "pie game" it, or whatever else you have to do. Do this twice if time permits, and then take a deep breath and start playing when given the cue. Once you've completed your audition, give any music you may have been given back, and leave the room, unless it was a recorded audition, in which case you may have to sit for a few more minutes to let them check the CD. .. it's over!
Don't let the environment get to you. If given the opportunity to test out the room, do so. Listen to the proctor. Play your sight reading material. Return borrowed items. Pat yourself on the back.