There were three phases to the process.
The first happened when I went to the store for an application. I filled it out in-store and handed it back to them, and a crew member pulled me aside for what was essentially a mini-interview. He made sure I understood every part of the job description, asked me why I wanted to work there, and what my favorite product at Trader Joe's was. Afterwards, he scheduled me for an interview two days later.
I arrived to the first interview a few minutes early, so they asked me to look around the store for a bit. 2 or 3 minutes later, a crew member came to get me and we headed to the back of the store, in the truck loading area. This interview got a bit more specific, and asked me about my previous work history, how I got along with previous employees, how I thought I would fit into Trader Joes', and what would be expected of me if I was hired. This interview took about 10-15 minutes. Afterwards, the crew member told me they would let me know in a few days whether I would go on to a second interview or not. They ended up calling me later in the evening, and I set up my second interview two days later.
I also came to the second interview a few minutes early, and was asked to wander the store again. The store's captain came to get me after a few minutes, and this time we went past the truck loading area and sat outside at a table behind the store. I was asked what appealed to me about Trader Joes', what I thought I would bring to the table as an employee, what I thought I would look forward to most and least, and more questions about how I thought I would get along with with other employees. This took about 15-20 minutes, and I was told I would get a call on whether I would be hired or not. It has been over a week now and no response, so it's pretty safe to say I don't have it.
Overall, the experience was very relaxed, and both of my interviewers were incredibly friendly. However, I can't give this a positive experience rating due to the lack of response after the second interview.