Amazon is driven by metrics, and interviews are designed to analyze how well you describe inputs and outputs. Questions will revolve around their leadership principles (which are public on their website). You'll go through an interview "loop", where you'll interview with several people from the proposed team. Typically, the people in your work group will be fairly easy to deal with, and are simply trying to get you to answer the specific leadership principle they are assigned to. Every once in a while, you'll get someone who's trying to be an arse for some reason, but if you know your resume backwards and forwards, and can pinpoint which principal they are shooting for, you should be fine. You'll finally meet with a director - who will be from another work group in order to avoid bias. The interviews don't have to be in order, though. The director was the second person I interviewed with in the morning, followed by two more in the afternoon. After the interviews, the group will meet to discuss whether you'll be a good fit. Ultimately, the director has the ability to trump the others, which happens all too often. They really want to see that you went above and beyond in your previous positions to make processes more efficient, that you have taken the initiative in the past, and that you will push hard for what you believe in (within reason and without hurting the group dynamic). In my interview, the director asked about evaluating the effectiveness of my time as a "Big Brother", through BBBS - which he found on my LinkedIn page. Pretty shady, in my opinion, but just be prepared to answer "analytically", anything that you list publicly (although I'm sure social media does not count). People WILL look at your Facebook page to get an idea of what you're about, so make sure to clean that up if you're serious about getting a job with Amazon (or anywhere else, for that matter).
It can be an intimidating process, but just pretend that the stuff you've done in the past is the most AMAZING thing ever, and you'll be set. Embellishment will be useful for you, and if you don't have numbers available to support your answers, simply make them up. For instance, "I helped develop a process that saved $150k over a 3 month span by doing 'x' and 'y'. Even if that didn't happen.
The interview questions are pretty generic "tell me about a time" nonsense, so probably nothing too surprising.