The interview process for Interns seems to be the same all around (based on other reviews on Glassdoor, and from friends). The initial interview is online, technical, and mainly focuses on debugging and logic questions. The second interview is also online and technical, but focuses more on being able to show that you have good database, algorithm, and OOP background. The final interview is over the phone with (for me atleast) a Software Manager at Amazon. I won't specify the question he asked me, but it required knowledge of OOP, database, algorithms, and general problem solving.
Here's a tip: I got nervous during my phone interview and failed to use the proper data structure needed, but because I asked alot of good questions and communicated with my interviewer throughout, I managed to get an offer from Amazon regardless. Communications matters.
Amazon was very quick with the entire process. I got an email for my first online interview, scheduled a time, took the exam, and got a response within 2 days. This was the case with all 3 of my interviews.