I have sat through many, many hours of theatrical auditions and it never ceases to amaze me how many actors, sometimes very good actors, fail to get roles just because they don't know how to present themselves in a professional manner.
At an audition you are a salesman, and you're also the product. It is your job to come over as an efficient and friendly professional -- someone who not only has the acting skills, but would also be a good person to work with. If you come over as surly, aloof, disorganized, or just plain disinterested -- why would you expect anybody to be interested in you, no matter how good an actor you are?
It is not difficult, but it really is worth taking a moment to reflect on how good a job you are doing in selling yourself. In fact, as an actor, this sort of reflection should be part of your stock in trade. Unfortunately, maybe because of the stress of auditions, many of actors fail to do this. Prepare yourself properly and it may just give you the competitive advantage in this very competitive industry.
Be on time and be prepared to stay. Always be on time for an audition -- in fact, arrive early to give yourself time to prepare and centre yourself. Arriving 15 minutes before your appointed audition time should suffice. Always try to keep your calendar clear for the rest of the day; if they ask you to stay on, it's a good sign, but it doesn't look good if you say that you have to rush off to another appointment.
Be friendly, but not too familiar. Even if you know people on the audition panel, do not try and exploit this by being overly familiar, this is a professional interaction. Remember, you want to show them that you are a good person to be a part of their company. Remember that this doesn't just apply to the people on the audition panel, you should be friendly to everyone you meet in the theatre including other auditionees. I have known actors fail to get roles because they were rude to the people who were helping to organise the auditions.
Be keen, but not desperate. Nothing puts an additional panel off more quickly than an actor who appears not to want the role. You should always seem keen and positive about the project that you're auditioning for. Even if you have reservations about whether this role is for you, this is not the time or the place to be expressing them. On the other hand, you don't want to appear too desperate, this will make an audition panel suspicious.
If things go wrong, handle it professionally. Inevitably, sometimes things go wrong during auditions. Even the best actors can forget their lines or trip over the scenery. If something like this happens, it doesn't necessarily mean that you will not get the role. If you handle the situation in a professional and confident manner, you may even impress people with your recovery skills. If you dry, then take a deep breath, re-centre yourself and carry on as quickly as possible. Never try to explain or excuse what happened, and never break into a torrent of expletives. Behave as you would if you were in a performance in front of a full audience. Never apologise or make excuses, people don't want to hear that you have a cold or didn't have long enough to prepare, it just sounds amateurish.
Look the part. Whether you like it or not, people will make judgments about you based upon your appearance. As an actor you can use this to your advantage by choosing your 'look' to reflect positive qualities. In general, your clothes for an audition should be comfortable, unrestricting and neutral or dark in colour. Avoid anything too risque, garish or formal. Footwear should be comfortable, avoid high heels unless the character necessitates this.
Flexibility is key. People want to see that you are flexible and can take direction. If you are asked to do something during an audition, always try to do it. By all means ask for clarification if you don't understand what is being asked for, but never argue or refuse to try something even if it sounds bizarre; they may just be testing you out.
Be organized and have materials prepared. Have an up-to-date copy of your diary with you at auditions. If people ask you about your availability, you will need to give concise and accurate answers. Make sure that you have copies of your CV and a head shots if appropriate. If you are providing both, then staple them together so that they don't get separated. If you have a business card make sure you have copies with you ready to hand out if required.
Remember your performance isn't just your two minutes on the stage; it's the whole time from your arrival at the audition space until you finally leave. If you do all these things you'll come over as a friendly, competent professional -- the sort of person that anyone would want in their acting company. Then all that you have to do is to demonstrate that you can act, but that's another story.