I went through U/RTAs two years ago. It's an interesting experience. Like Matthew said, you do your interviews in hotel rooms, which is a little weird.
So... the U/RTA process...
Bascially you put together a "common packet" which consists of your URTA app, resume, examples of paperwork, sometimes essays about what you want to get out of grad school, etc. You send each of these common packets out to the schools you want to go to. Then you call each of the schools to make sure they received your packet and find out if they want anything else from you. So in a sense it's like showing your portfolio, only through the mail and less specific.
Then, URTA lets you know which schools you have interviews for and what time the interviews are. What frustrated me about this is that I wasn't told until about 2 weeks before the interview dates. So, I was glad I wasn't buying a plane ticket to Chicago with only 2 weeks notice - I was driving.
The SM interviews I had were basically the head of the SM department explaining what their school's program is like and then asking a few questions. Some of them ask to see your prompt book, but they don't spend much time on it. Some ask to see your resume again, so it's good to bring extra copies. Some of the questions are about stage management theory (which I enjoy more) and some are very practical (what would you do in this situation).
I did get into an URTA school. I'd say what helped me get in was persistence (I applied the year prior when they were only accepting 1 student and chose to apply to my school again rather than accepting anythingelse), and bringing in questions of my own about the program or stage management. I ended up having a sort of mini-seminar with the head of my department at my interview. I asked him a sort of what would you advise your students to do in this situation question that I wanted an honest opinion on and that sparked a good conversation. So, persistence and drive, I think.