I applied through an employee referral. The process took 1 week. I interviewed at Trader Joe's (San Jose, CA) in Mar 2012
Interview
Brief since I knew the manager. they pretty much walked me in and told the captain that i was being referred. Asked a couple of basic questions but nothing out of the ordinary.
Applied online and had one in person interview with the captain. It lasted maybe 10 minutes. Got a call a week or so later that I got the job. Very fast process.
It's two to three interviews, the final with the Captain (or highest manager) of the store. The interviews are largely to get to know your personality and how well you would do at customer service.
The interview process was absolutely wonderful! I didn't feel stressed or nervous and it felt like I was just chatting with a friend! Trader Joes is a great company and the interview was great.