Check the audition's requirements very carefully. They may ask for resumes, head shots, a particular sort of outfit, or an understanding of the type of film being cast. Make sure you have everything they require, and don't be afraid to ask your agent or the audition's contact if there's a requirement you don't understand.
Prepare a monologue from a play or movie similar in nature to the one you are auditioning for. Try to tailor it to the character you're up for. If you can, get a copy of the script itself and select a scene out of it. Memorize it before the audition, but at the same time, don't become utterly dependent on it. They may ask you to show an entirely different set of emotions during the audition, in which case you need to think on your feet and be ready to give them what they want at a moment's notice.
Arrive early at the audition to fill out any paperwork and perform any warming up exercises you require. That way, you'll be ready to go when they call your name and can perform without rushing about.
Listen to instructions given by the casting director to other auditioning actors, if applicable. They may involve details which you need to know, such as shifts in the content or time limits on a given monologue.
Project confidence and assuredness when the time comes for your audition. Look the casting director directly in the eye and respond politely and courteously to any instructions they give you. When you're done, thank them for the opportunity and give way for the next actor.
Put the audition out of your head while waiting for callbacks. Fretting and worrying doesn't help anything, and if you don't get the part, there's no need to make the disappointment any greater than it has to be. Move on to the next audition--or whatever else is in your life--and try not to stress about the one you've just done.