Such a stellar, stellar process. I was floored by how efficient and enjoyable every step was. I applied through an employee referral after meeting several employees at a conference. Because of NDA, I will remain pretty vague here--but several months later, they began looking for fall interns and a university recruiter contacted me saying she had received my CV through an earlier referral. A week later, we had a 40-minute phone interview (essentially a prescreening on what you're looking for, what experience you'd like to have, why Facebook, and most particularly what your research entails). Three days later, I found out I'd moved on to the next stage.
Two weeks later, I had a 50-minute Skype interview that was based on behavioral questions, more about my research, and a few curveball questions that make you think much more deeply about research and methodology. I found out that day that I'd moved on to the last stage.
Two weeks after that, Facebook flew me out for an on-site interview. Keeping this as vague as possible, I will say that they were so incredibly gracious and did so much to make sure I had a good experience (it would be hard not to!). Everyone I met was awesome, the campus is fantastic, and everything was incredibly efficient. Expect a presentation on a surprise prompt (you have three days to prepare) and one-on-one interviews.
When I left, I realized that even if I didn't get this, just the experience of that single day made everything worth it. Good luck!