Choose a song that fits your voice. The judges may have given you some guidance on what type of song to sing, and you should try to follow that guidance. However, make sure you find a song (and key) that uses the richest part of your voice. You will find a resonance as you sing -- coming from the notes as they echo in various parts of your chest and throat. Identify these notes and find a song that uses them.
Memorize the lyrics. You can't afford the distraction of grasping for forgotten lyrics; you must focus on vocal production. Make sure you know the lyrics perfectly so that you can give your full attention to making your vocals as clear as possible. Rehearse the song enough that you do not need a lyric sheet to review before you go into the audition room.
Sing daily before the audition. Your vocal chords need a constant workout so that they can be at their peak when it's time to sing. Your voice is an instrument, and you can't expect to sing your best when you have not kept your instrument in good shape. If you get a spur-of-the-moment audition that will not give you enough time to sing for a few days in advance, let it serve as a reminder that you should always be prepared through daily singing.
Warm up right before the audition. You can hurt your voice if the vocal chords are not prepared for the intense notes you must produce. Even if other singers are around, find a corner and go through your vocal warm-up exercises. Focus on the clarity of your tone, not the volume of your notes. Gradually increase the volume until you feel you have the strength to produce loud notes that do not warble or become muddied.
Sing to the echo, not to the judges. Every room has a natural reverb, an echo that will bounce back to you as you sing. Focus on this echo so that you are attuned to the sound of your voice. You can smile at the judges and make eye contact, but don't focus on their faces to determine how you are doing. The sound you hear bouncing back to you should be your guide that lets you know how well you are singing.