I had 3 rounds - a written, phone, and in-person interview. It may be 2 now, not sure about that.
I forget the specific questions, but just really understand what you are applying for. You have to show a strong commitment and that means things like talking to alumni and corps members, visiting schools, reading TFA blogs, learning about the education situation in the US, etc. If you can not put in that effort before the interview, there is no way you will survive the job.
Beyond this, most of the interview is behavioral - be able to talk about your experiences well. The questions were fairly standard, but just be prepared as it is difficult to think about anecdotes/examples on the spot.
The biggest difference between TFA interviews and most other places Ivy League kids apply to is that for TFA, you need to show that you really care about this issue and that you're a nice, humble person. You can survive a top consulting firm or I-bank being a jerk if you have strong analytic ability - but with TFA, no amount of smarts will help you if you can't get rid of your ego.
Finally, I'd recommend not trying to be someone you're not. If you need to put a persona to get into TFA, you're not fit for the experience and you're not going to like it. You can BS and tolerate your way through a corporate job to get to the next step in your career - but don't take that approach to TFA. TFA is an extremely tough but rewarding experience that requires an incredible amount of commitment to the cause.