1 Don't do monologues from movies.
If you do a monologue from a movie, people will automatically think 'not like in the movie'. That will make them think negative things, and because you're not like the actor/actress in the movie, they'll most likely think less of your ability.

2 Don't do very well known monologues.
Pieces like the 'To be or not to be' speech from Hamlet, or something like that, the directors have seen those all the time. They get tired of seeing that. It's not unique anymore, and they'll lose interest fast. Do ones that haven't been performed enough, or better yet, one you think they've never seen before. It won't bore them to death and they'll like you've taken the time to find something unusual.

3 Do pieces that fit you.
Make sure that your monologue is relatable. Ask people what their first impression of you is. If you get things like 'ditzy popular cheerleader' (sorry, just an example) then a piece about someone like that would be good for you. It looks better than if you do a piece about an old man (unless you're that good an actor) but keep to what others see you as. In theatre, appearances DO matter.

4 Make sure your monologue is a good length.
Unless they specifically ask for a certain time, use a piece that is from 30 seconds, to 2 minutes.

5 Don't worry, be happy.
They don't tell you this, but the minute you step into the room, you are auditioning. The directors want someone that's fun to work with, nice, and responsible. The directors are watching everyone, to see their personalities. If you're smiling, talking with people, and in a good mood, they'll like you. If you're sulking in the corner, or being rude or too cocky, they won't like you as much. Help out if someone needs it, and when being introduced, look people in the eye, and use a firm handshake. Sometimes the director doesn't care about your monologue at all. They just want to see what you're like. But still give your all in the piece, because you never know what's going through the directors mind. Above all, smile as much as you can while making it look natural, and be yourself!

6 Enunciate.
While performing, pronounce your words clearly. If you're character talks fast, the director will care more about what your voice sounds like and if they can hear you. Go slowly if you can, and speak loud. They want to hear you. You can put so much emotion into your piece, but it's lost if they don't know what you're saying. Water will help clear your throat. Before an audition don't have milk or yogurt or anything with too much dairy; it will get mucus in your throat and you won't be able to speak as clearly.

7 Be calm.
While introducing yourself, speak clearly and don't fidget. This will show them you are uncomfortable and don't want to be there, whereas if you're confident, head up, looking straight ahead they'll think 'Oh, they really want to be here. They can commit to characters.' And don't step backwards in introductions. That's a sign of weakness. It's a case of the strong survive. A calm, confident exterior will show enthusiasm and eagerness. If you're looking at the ground, or not making eye contact in introductions, they'll think you have a problem with being there.

8 Look over your audition.
Make sure you know what your piece is about, what is your characters story? What's going through their mind? And make sure you know how to pronounce everything. I once had a piece where is says "RAM". I thought it meant R-A-M, instead of ram.

9 Don't creep the director out.
While introducing yourself, you may look them in the eye, but while performing if you're staring at them, they'll get freaked out.

10 Emotions.
Get as wide a range of emotions into your piece as possible. Try to show your range of abilities. Fid a piece that can let you, or you can manipulate so you can act sad, happy, grief, anger, confusion ect. Be as creative as possible and don't stick to one emotion in the whole audition. Be flexible and change each beat between paragraphs if you can.

11 Take risks.
If you're doing a piece about someone who's grieving, try to see if you can do a dry laugh somewhere in it. Try saying parts different ways. See what feel best.

12 Congratulate yourself.
I If you don't get in, still get yourself some ice cream or something as a reward for trying. If you don't be depressed about not getting in, it will make you feel better next time you do an audition. Keep trying and eventually you'l make your big break.

Above all, have fun!