Hiring process is like any fortune 500 business, they take your application and is processed by a third party. They email you saying they'd like a phone interview, and if you agree they setup an appointment. Mine happened to be at 2PM on a Thursday, and they called at 2PM, not half an hour or an hour later like someone else mentioned.
They ask you questions such as 'What was your most stressful situation?' and 'Have you ever done something without having to be asked to do so at your last place of employment? And if so, what was it?' After a few questions, they thank you for your time and tell you if they selected you that you would be getting an email from Amazon.
About 2 weeks later I got an email for an in-person interview. I get to the location early and it's full of other people being interviewed. You approach a desk, they ask your name and ID, pull a piece of paper with your schedule, name and email on it. They ask if everything is correct, if it is, they enter you into the system and give you this piece of paper. Once you're called, you are escorted by an Amazon Day-One employee to a management employee, it's extremely casual as all the interviewers and Amazon associated employees are wearing short sleeved tshirts and jeans. Introduce yourself, they introduce themselves and explain who they are, how long they have been with Amazon, where they started and what their current position is, it's an extremely open interview. They ask you the basic questions 'What would you do if you saw someone steal something? What would you do if it was your best friend?', 'How do you handle stress and fast paced environments?', 'What was the most stressful event of your past employments?'. As you answer the questions, your answers are being typed into a laptop, they don't hide it. Once the questions are finished they ask you if you'd like to ask any questions regarding Amazon. They mark a piece of paper that was given to them by the escort from earlier, and this mark is what finally determines your employment, if you should be hired or not, or if you should be interviewed again.
Once it's finished, you're taken to a waiting area, and are finally told to relax and sit back, you got the job as long as background check and drug test come back in your favor. You then enter a room, have your ID picture taken, sit down with the rest of the group and continue on. At this point, they explain the history of Amazon, the goals of Amazon, their focus and who they look for. You do the drug test, and are able to leave.