The interview at the location is conducted by one of the instructors -- these are all guys who have gone through the program, so they can really give the some great insight about it. After filling out some paperwork (total time, education, type of A/C flown, etc.) and grilling the guy/girl with all of your questions about ATP, you will have to take a 50 question multiple choice test. If you haven't gone over your PPL stuff lately, I would suggest you brush up before going there. It includes aerodynamics, airport markings, wake turbulence, aircraft systems, pattern work, uncontrolled operations, comms, etc.
Once you've taken the test, the instructor will put you in the sim and have you do some basic flying -- take-off, turns to headings, climbs, descents, etc. He'll then explain the engine out procedures on the Seminole and give you a few chances to try it. They are not looking for you to perfectly nail the checklist and recover from the lost engine -- they just want to see that you have a basic pilot's knowledge and are teachable.
If your interview goes well, you will be recommended to the program and a phone interview with Jim Koszarski (VP of ATP) will be set up. After asking about your background (where you got your private, what A/C you flew, your education) Jim will cover some of the same PPL stuff, as well as some basic multi-engine critical engine factors -- if you read about and can describe P-Factor, accelerated slipstream, spiraling slipstream and torque you'll do great.
If all goes well on the phone with Jim, he'll offer you a slot -- it's then up to you to tell him when and where you want to start. If there's an opening, he gets $1000 from your credit card and you're all set. If not, you can pick a different date/location.
After going through the program, I really appreciate the fact that ATP isn't just taking money from anyone who wants to go there -- by requiring people to jump through a few hoops, I think they get a much more committed group of pilots.