Be Prepared for the Audition
Once you know what is expected of you, get ready! Choose your audition song and audition monologue appropriately. If they want to hear you sing a song, memorize the words. Same goes for a monologue or scene. Know the song inside out. When you get to the audition, if you know the song cold then it will be one less thing to worry about. If you will be doing a sight reading, read the play you are auditioning for, and ask yourself, "If I were a director, what scenes would I choose for auditions?" You'll be suprised how often you're right! Also, practice reading lines you've never seen before -- it doesn't matter what play they're from. This will increase your ability to act well the first time you read something. This is an important skill, because some auditions and most callbacks will ask you for a cold reading. Don't forget to warm up before the audition! There will be a lot of people to see, and the auditors won't have time to wait while you work the phlegm out of your throat.
Get to Know the Audition Space
Whenever possible, try to find a chance to familiarize yourself with the audition space and how to get there before you actually go to the audition. If its in a theatre, go and see a show there, or attend a rehearsal for a show. If it's not in a theatre, you can still find a way to sneak a peek. Pretend to be a tourist, or just beg your way in. Being familiar with the space (and knowing how to get there!) will ease a lot of stress on the day of the audition. Make note of how long it took to get there so you can be sure to leave in plenty of time for the audition. Keep these notes in your audition log book.
The Audition Panel Is NOT the Enemy
Try not to think of an audition as a war zone. It is not "them against you." Try to think of it as a chance to see if you and the directors would make a compatible team. Your song or monologue isn't the only factor deciding whether or not you will get the role. They also need someone who will be easy to work with. If you have any questions about the show, don't be afraid to ask them. It will show that you are genuinely interested in the production whether you get the role or not.
Take Comments From Others With A Grain of Salt
Yes, we should assume that all the people we will meet at an audition will be nice to us, but this isn't always the case. Remember that the people you meet in the waiting room may be auditioning for the same role as you, and may have personal reasons for saying things that might scare/anger/discourage you. Don't let anything that someone else says distract you from what is really important. When you are waiting for your audition, concentrate on being calm and prepared and avoid gossiping with other auditioners.
Concentrate On The Audition As A Performance
Remember that an audition is essentially just a performance for a very small audience, and you should think of it that way. Presumeably, since you want a part, you actually enjoy performing, so try to bring that enjoyment to your audition. Also, make sure you are maintaining your focus by thinking in character. If you are thinking what the character you are portraying would think, you won't be critiquing and worrying about your performance.
Also, make sure that your audition pieces are up to performance quality. Try to avoid using new pieces in auditions if possible, because pieces that you are less experienced with are more likely to make you nervious.
Remember, however, that the audition panel has a job to do and they are not there to be entertained. Do not expect them to laugh or applaude.
Be Realistic About The Audition Process
Auditions are a nervewrecking experience for everyone. Come to terms with the fact that you are unlikely to give the performance of your life in an audition. Similarly, allowing yourself to stress over things that are out of your control (such as what "look" the audition panel is looking for, or how competent the accompanist is, or how tall you are) will cause you unnecessary nervousness because there is nothing you can do about it. Concentrate on doing your best in areas in which you do have control - memorizing your monologue, choosing an appropriate song, and preparing for cold readings. When you feel prepared, you will also feel confident.