There are many steps. First, I submitted my resume to Amazon via my college's hiring website. Then, an Amazon recruiter contacted me saying they liked my resume. They had me take a culture fit survey. Then, I was contacted to do a 30 minute phone interview. They do two math problems in the phone interview. I got 1/2 correct - I made a small error on the first one. They care more about your logic and if you can explain why you did something, rather than if you got it correct.
Next, I was contacted to do an in-person interview. They flew me to Wisconsin, set up my flight, rental car, and hotel. Some people said they received an e-mail saying that Amazon would pay for up to $60 for food and other expenses (I did not receive this e-mail). Kinda bummed about that, but no big deal. Made it to the interview. There was about 10 other people there. They took us all into a room and gave us a math flow problem to work out. Gave us about ten minutes. After this problem, I was taken into a one-on-one interview with an ops manager and I had to tell him what my answer was and how I got it. Once again, I got the problem wrong but he made me realize where I had messed up and I had to correct it and re-do it in front of him. Thankfully, I got it correct.
Then he had me role-play a scenario about how I would work with employees being late/issues.
Then, I had one more one-on-one interview. Each of these were about 30 minutes. This interview was more of the STAR method
I flew back home and two days later I had my offer letter e-mailed to me.
**I say the process took so long below only because the recruiter and I had trouble finding a time for me to fly out to do the in-person interview.