Here is what I tell my students about auditioning.
1. Be prepared. Music.
This means having music memorized, music marked clearly for accompanist, having a point of view about the character. The assumption here is that you have already worked out the technical aspects of any piece that you offer for an audition and won't have to worry about that at all. An audition for a role is very different from a singing competition or an audition for entrance into a program where voice is everything. You want to present a complete package here.
2. Be prepared. Dress.
Dress appropriately. You don't want to be remembered for how you dressed for your audition - either in a good way or a bad way. You want them to remember your performance. People have VERY different ideas about what is appropriate for an audition. I have a friend who insists that all her female students wear stockings any time they sing.
This is certainly a place to use your best judgment based on specific information you might have. However, when in doubt, wear something conservative that flatters your own shape.
3. Be prepared. Information.
Know what the company wants to cast. If possible, know the upcoming season and which roles might be right for you. Bring audition repertoire that reflects an awareness of this information. People have differing opinions about whether or not to offer something from one of the shows being produced. Use your best judgment here.
4. Be prepared. Know what the company wants to hear.
In other words, be prepared with the information and repertoire that the company specifies in the audition announcement. If they say they want 16 bars of a piece of music - offer 16 bars. This is especially important for those who are used to doing opera auditions (which traditionally hear more singing) who are participating in a musical theater audition (which traditionally hear comparatively little singing). If a monologue is requested, find and prepare a spoken monologue. If a dance portion of the audition is specified, bring appropriate attire for a dance audition.
5. Be prepared. You might not get the part you want.
You might be offered a different part than you anticipated. Know before you audition whether or not you can accept larger/smaller roles. The company representatives may ask you at the audition and it is considered bad form to misrepresent yourself here.
You might not be offered a role at all. Remember, this doesn't mean that the company didn't like you or didn't think you were worth casting. It may be that they liked you but just don't think you are right for anything that they have available this season.
Are you sensing a theme here?