I applied through a staffing agency. The process took 3 days. I interviewed at Amazon (Minneapolis, MN) in Sept 2015
Interview
Large initial hiring group before opening. The interview process has without a doubt changed. Speak to your local employment agency or apply directly to Amazon.com Much of the process is paid hours of video simulation, drug testing, policy/disclosure agreements, and formal I9 forms, etc. to fill out...
No interview at all, you go into the hiring center, take your drug test, fill out some preliminary paperwork, verify the building and schedule you want, your start date and that's it.
Not too bad pretty easy and straightforward, simple question surrounding handling and moving. Make sure you know basic safety rules as they will ask you, for example how do you carry heavy items.
Apply online, go to the on-site office for oral drug swab and ID picture. Start date is assigned once background check comes back. The actual start date will depend on how fast the check comes back but isn't normally delayed.