I applied for the position in January and received an offer to interview about three weeks later. I was in school in California at the time, and they flew me out to DC to interview. The logistics were very well planned. I flew out the day before, and stayed the night at a hotel. The next day, I met early with the current predoctoral fellow for breakfast, and then I had a series (two or three) of half an hour, one-on-one interviews with researchers in the department. I then gave a pre-prepared talk before the entire department (probably about 20 people), and fielded questions, lasting about an hour. In the afternoon, I had a couple more one-on-one interviews, and flew home.
The whole process was fairly exhausting, and certainly more than I'd ever done before, as this was one of the first full-time jobs I ever applied to. Though I think there were probably more interviews than really necessary, I think the way the interviews were conducted was very appropriate for the role-- someone who could think creatively and critically about ethical issues in the sciences. The questions I was asked were very intellectually stimulating, and the interviewers did a really great job of speaking to me with a great deal of respect even though I was probably rather underqualified for the position and I was espousing a point of view that's not very popular.