I applied through a staffing agency. The process took 2 days. I interviewed at Amazon (Moreno Valley, CA) in Aug 2014
Interview
At the start (remember it's casual/business casual) you go into the recruiting center to sign in and wait (this can last a few minutes to a few hours). The interviewer will call you in for the interview. The questions are the basic questions in an interview. After that, they'll send you back into the waiting room to do their screening process. Once they call you up you take a little survey, do your drug test and fill your W2. After all that is finished, they'll send you on your way and tell you they'll call you for your follow up.
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.