I've auditioned several times. It might be my TR you're referring to.
I've never actually made it backstage, but here's what we experienced.
You go to the audition area, which is directly across from the Sci Fi Dine In. The CMs there have a list of songs to choose from. If you are over 14, but under 18, you must have an adult with you (doesn't have to be a parent, just an adult).
You take the list and go up to a doorway (I've only waited maybe 5 minutes max to get in the door), then once inside they show you a video of Ryan Seacrest who encourages you to "enjoy the AI Experience).
Then you go stand outside an audition room to wait for an open CM. Each audition is inside a small room. The CM is sitting behind a desk, and there's one upright chair in the corner. The CM will chat with you a little bit, asking about your musical experience, etc. They then ask you to sing about a 30 second clip of any song you like. The only requirement is that it can't be an original song (i.e. one that's unpublished). Everything in this room is done without accompaniment, just your voice.
If they like what you've done, they'll ask you to pick out something from the song sheet. In some cases, they will hand you a word sheet and give you the starting note. They also have audio clips of the recording if you ask them.
If you do well at this point, they ask you something like "are you going to be here most of the day? Do you have time to meet with our producers?" In that area, you're given an IPod track of the song you've chosen, and given time to practice before you meet the producer. That's in the open area outside the casting rooms, so you'll hear people doing this while you're waiting for your audition. The director's audition is done with a vocal track.
At the point where they decide you don't make it, they'll give you constructive feedback on your performance. Examples I've heard include: You need to work on projecting in your "head voice" range so it matches your "chest voice". You need to show more vocal range (i.e. high to low) in your audition song. You have a beautiful choir voice, but it's not a pop sound. My son has been told to develop a bit more confidence, to avoid singing through his nose (unless it's a country song), that he has a good sense of the rhythm, but needs to stay on pitch. My DD has been told that she changes key in mid-song (which she does, especially without accompaniment).
The very first time we auditioned, I was asked to see the producer (which is why I know how they phrase it), but we had other people with us so I passed. Since then, I haven't made the cut,but I've learned something each time. I'm never going to be on that stage, but I'd like to at least get to the producer to see how that works.
The best odds are early in the morning. They want to fill up those early shows, and there aren't that many people coming into the auditions early enough for the 11:00 show. If you audition after about noon, unless you are a soloist quality singer you probably won't make it. You can see the difference if you watch different shows throughout the day. By the time you get to the 6:00 show (the one before the finale), all the contestants are pretty good.
Good luck and enjoy the "AMERICAN IDOL EXPERIENCE!"