I applied in-person. The process took 4 weeks. I interviewed at Trader Joe's (Los Angeles, CA) in Jan 2014
Interview
This is a one-on-one interview with either the captain or mate. The 'captain' is the head supervisor who runs the whole store. The "mates' are shift leaders who help maintain the whole store. They're usually friendly and open with you so you don't feel intimidated like you would with other companies.
It was quick and seamless and they let me know in ample time. It was a painless process and the crew was quick to give honest opinions about working there. The Captain changed but at the time turnover wasn't high.
Interview questions [1]
Question 1
Why do you want to work at Trader Joes and do you have any favorite products.
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.