Have a singing history, such as singing in a choir. If you haven't been regularly singing your whole life, you won't have a chance to win. You could still be picked for the show, but likely to be the spectacular failure for ratings.
Stand out from the others. Know what your most outgoing personality is--whether it's sweet, goofy or vicious--and turn up the volume on that personality.
Improve yourself as the show progresses--not just in your performance, but also in your appearance. Carrie Underwood and Fantasia (and nearly Clay Aiken) won partly by going from plain to glamorous.
Be courteous to and support the other contestants, but remain confident in yourself. These people usually win over the ones who are excessively self centered or humble.
Remember that Randy is the judge to impress the most. Paula is easy, and Simon is near impossible. The ones you must impress the most, however, are the viewers.