Oddly enough, as a trained singer, i'd probably be the most likely candidate to give you advice on this topic - but unfortunately, my total disdain for the show handicaps my ability to really give much insight into the whole process in terms of what works and what doesn't and what they're looking for or even largely how the entire process/set up is. If you're confident enough in your ability to audition for AI, i trust you're already well versed in the basics and already know excellent and essential audition techniques (make sure you're well-rehearsed and voice fully warmed up well ahead of time but also that you haven't overworked your voice the week leading up to it...be well-rested (but also fully awake) and voice kept warm and lubricated with warm non-caffeinated liquids.)
So in place of that, i'll instead provide the best advice i can give that really doesn't even have much to do with the singing: think long and hard about all the possible implications being on a national reality show entails and be very clear that you're okay with it and that you really want to do it beforehand. Whether you make it to the show itself or just even seen audtioning on camera, how much do you want whatever particular moment that gets shown on screen to be your "15 minutes of fame" and the thing that you'll always be known, remembered by, and labeled as for the rest of your life, decades after the fact? And that's even if you're seen for less than five minutes. If you make it as a contender and are on the show for several weeks, how much do you want to sacrifice any and all privacy or have anything at all that's part of your personal life (even your family's personal lives) considered fair game for bloggers, tabloid/gossip press? If you have serious plans of being a professional singer, you will always be first and foremost thought of by both the public and the industry as "American Idol contestant/(winner, third runner-up, etc)" and need to be prepared for how that all-consuming label will always color people's expectations and how seriously they take you. Especially given that your mass introduction to the public will be via a show/entity that's all about shaping talent into a particular mode and if you thrive on individualism and personal expression/artistic freedom, that may be just as big a curse as it is a blessing, if not much more so. Whatever your career/personal life goals are, be they entertainment-related or not, if you have any level of success, be prepared to never really ever being able to know or trust if each new person that enters your life is liking you for yourself or the fact that you were the guy who reached whatever level on American Idol - that will always be an essential permanent tattoo on your forehead that everyone will judge and know you by before they ever actually know you as a person.
Myself, i would never remotely consider the idea (of that or any other reality show, talent-based or not) as the cons far outweigh the pros to someone like me that values my privacy and artistic integrity too much to have it reduced to a pop culture soundbite or stigma-heavy label. Singing and performing has long been my life but being on a show like American Idol would be one of my worst nightmares. Be sure that you enter into the situation eyes wide open and fully aware of how it can follow you the rest of your life.