I applied online. The process took 2 weeks. I interviewed at Kroger (Alpharetta, GA) in Oct 2012
Interview
Very easy interview. Basic questions asked, no surprises. Asked about availability (fuel center hours are 6AM-11PM). Asked about why I want a job. Asked about experience with customer-facing jobs.
No negotiations for salary; Kroger is a union shop and usually there are set scales for pay in different jobs.
Advice for an interview with Kroger: be friendly, dress nicely, arrive a little before scheduled time, say "please", "thank you", and (if appropriate in your area of the country) "yes ma'm" and "yes sir".