I applied through Zappos' website. The initial application process involved the usual resume and cover letter as well as a simulated project where I was asked to map out how I would introduce a new product to Zappos' website. This was to test project management skills and critical thinking. Then I had to complete an automated interview where I was prompted with questions and answered using my webcam and microphone. It was a little weird talking to my computer, but nothing too bad.
They emailed me back a few weeks later to tell me that they were flying me out to the Las Vegas headquarters to see the company and interview as a finalist for the position. The recruiters were extremely helpful and helped take care of all of the logistics and costs of flying there and back.
The Zappos headquarters is out of this world cool. The first day was very relaxing and they didn't drill us with any interviewing. They welcomed all the potential interns and took us around the campus and introduced us to the Zappos family. I got to see all the different departments and witness the company firsthand.
The interviews themselves were two parts, a technical interview and a character interview. Zappos believes very strongly in maintaining its corporate culture and will disqualify someone if they fail the character interview even if they ace the technical interview. The TPM team was very accommodating and answered all my questions during the simulated project. the recruiter for the character interview was also very friendly and not at all aloof or adversarial.
Zappos has a corporate culture that all companies should emulate. It's a fantastic place and I would encourage anyone to apply there.