First initial interview is usually with the PT Director of the Club. He may have you on the spot, take a piece of paper, and tell you to walk the fitness floor and get 5 different people's thoughts on why they joined the club and tell you to come back.
If you make it to the next stage, you come in to train one of the trainers, who is typically an Assistant Director (can be anywhere from 3-6 of these depending on size of club). Be ready for them to throw a monkey wrench in whatever you had planned (will possibly act as if they have bad knees, ankle injury, etc.) If you are lucky, they will just want a good workout, because typically it is their down time when they usually workout anyway.
The third stage is usually with the GM of the club who oversees the entire club. Be ready to know information about the club. My GM asked me on the spot what the mission statement was, word for word. I was given a heads up by the 2nd interviewer. Also, depending on the person, (my GM was a little different), asked random fitness questions, such as how many bones in the body or something random like that.