There's an initial phone screen from a recruiter. Following that, there's a code submission process, which precedes a more technical phone screen, which in my case was conducted with two members of one of the engineering teams. If you pass all of those, then there's an onsite interview that's quite lengthy (all-day). There are a variety of different sessions that evaluate general technical background, product design, and pair programming ability. Keep in mind that the onsite is a long day and the pairing session is done towards the end of your interview.
To echo some of the other interview entires here, the types of questions are really geared more towards practical experience as opposed to purely 'academic' scenarios (which I found refreshing). You'll speak to quite a few different people; everyone that I spoke with was great. I felt like I was able to develop a good rapport with all of the folks that I met. In general, I think the content of the interview was pretty well thought out and well-rounded.
Overall, the interview was challenging but not overly difficult. I was fortunate to work with an excellent recruiter who was prompt and courteous throughout the entire process (which was rather lengthy due to the holiday season). I met close to a dozen people at Braintree during the process and everyone was really pleasant to deal with. Despite the fact that I didn't receive an offer (which is also something I completely respect - I definitely recognized mistakes I made during the onsite pairing session), I'm glad I had the experience of interviewing at Braintree.