My process is probably a little different from others. I got hired from my school's career fair (which I used to think was a pointless thing to go to).
I just made sure that the people tabling (which ended up being my team) knew that I was VERY interested in Amazon even before I saw them at the career fair. I sent them a few before-fair emails, talked about my projects at the fair, and sent them a few more emails post-career fair. A few weeks later, I got an email asking if I wanted to have another phone screen.
The phone interview was surprisingly 'unorganized.' The guy I talked to just mentioned what the team and location I'd be working at is like, and gave me a talk on the hierarchy of the org. I never talked about my projects or who I was (though that may be because I already did at the career fair.)
After a week of silence, I was invited to come in for the final on-site interview.
The recruiter told me that I would have to prepare a presentation, which he later followed up with a call about the details of how I should prepare. Even the manager who would be interviewing me onsite called me to ask if I had any questions while preparing, which I thought was very considerate.
The onsite consisted of an hour long presentation of my work (I recommend using Keynote!), followed by lunch with a buddy of your choice, and 5 one-on-one interviews with no breaks in between. It was exhausting, but everyone interviewing me knew it was, so they were very accommodating, which made it bearable.
By the last interview I had no idea what I was saying, but overall I felt pretty good with myself.
They told me they'd get in touch, and 1.5 weeks later, I got a call from the recruiter offering me the position!