In the past, the process has been to complete essay questions. You're limited to a specific number of words, and it has been three questions. There have been three rounds in the past, including two rounds of essays and a telephone interview.
The process isn't terribly painful, but I will say that I agonized over how to answer the questions! It can be tough when you think about what they WANT you to say as opposed to what you FEEL.
Good luck to everyone thinking of applying! And I want to say, the spots are so few and the applications so many. I know that anyone I have EVER encountered here on the DIS is certainly qualified to do this job. Please don't be discouraged if you've applied before and not been asked to round 2 or round 3. The people here are helpful, knowledgeable, and downright nice folks!