Read the script of the show, because understanding its premise and the character you hope to play are essential to a good audition. Prepare the required monologues, which can vary from one of less than 60 seconds to two minutes for two contrasting pieces. Always have an additional piece prepared in case you're asked if you have anything else. Bring your headshot with a resume attached to the back. The headshot should be current and the resume an honest reflection of your skills and experience.
Wear comfortable clothing that's flattering in fit and color, and suitable for the class of the character you hope to play. Never wear a costume. You want the person casting to be able to see you in the role, but the wrong costume may prevent him from seeing beyond the wardrobe choice you've made. Be polite and positive throughout the entire audition. Directors are looking for someone who brings a lot to the role but can also be flexible enough to take direction. Don't forget to breathe. No matter how nervous you are, breathing will keep your voice even, your posture solid, and your thinking sharp.
Have additional headshots or business cards at hand when you leave an audition; you never know who you'll meet. Like you would do after any job interview, follow up your audition with a thank-you note or email to remind those making the casting decisions of who you are and thank them for the opportunity. If you receive a callback, be prepared to continue showing them your flexibility, range and positive attitude.
Don't let a little rejection set you back; many very successful actors experienced a lot of "no's" before they broke through and became stars. Learn from the experience, and reflect on how you performed and how people reacted to your choices. Make necessary adjustments and go the next audition with an added sense of confidence.