Select audition monologues that move you and tug at your emotions. Remember that you'll likely be performing your chosen piece over and over--you don't want something that will start to feel stale or false.
Choose a section of the monologue that is equal to or slightly shorter than the allotted time for your audition slot. The standard length is roughly 2 minutes per monologue piece, but different auditions may have different requirements. The director or producer may cut you short if you go over the official time period.
Edit out parts of your monologue if you need to pare it down for timing purposes. However, take care not to cut anything that gives vital information about your character. Instead, skip language that refers to other parts of the play and expository details that aren't required to understand your character's emotional state at that particular moment.
Look for a monologue in which the character undergoes some kind of psychological movement. Since your performance will likely be short, this shift may be a small one, like deciding to make a daunting phone call. What matters is that you demonstrate your ability to transition from one emotion to another in a believable way.
Take care to select a monologue that shows off your strengths as an actor without being too narrow. If you're good at being funny, make sure your piece includes some humor--but it should be complex enough to hint at your serious side too.
Think "memorable." The casting directors will likely have to sit through dozens of audition monologues, and you should look for a monologue that sets you apart. That doesn't mean selecting something off-the-wall, but something interesting and true that you can deliver with conviction.