The actual interview was relatively quick; it was a 1-hour one-on-one with the general manager hiring me. I did not meet with anyone else or have to provide anything else. I didn't actually start the job until 6 weeks after that interview; Delta's hiring process takes at least 3-4 weeks to get someone in the door, as I confirmed when I hired someone a year later.
My first impressions were of a disorganized place--it was unclear which building I was supposed to go to and where exactly I should meet the hiring manager; entering the admin building, I was greeted by an empty lobby, as Delta no longer employed a receptionist.
As far as the actual interview:
Delta's approach is to give you an overview of the job and its requirements to ensure you understand what you're being interviewed for. Then it's a review of your resume and experience to get some idea of your background. Then the interviewer moves onto situational questions ("Tell me about a time you...", "What was your biggest challenge and why?", etc.) and hypothetical questions ("Imagine you were asked to do <blank>; how would you respond?").
The interviewer tends to be quiet, listening and taking notes, although I swear mine was actually checking their watch and e-mail occasionally! I did get a chance to ask questions, although I think the level of interest and detail was a bit unexpected for the hiring manager.
I did not get a chance to meet anyone else or tour the facilities--it was very much just sitting down with the interviewer, answering questions, and asking some questions.