I applied in-person. The process took 1 week. I interviewed at Publix (Canton, GA) in July 2010
Interview
You take a drug swab right there in store, then wait a week to get setup for orientation. Interview process is very informal with the store manager and department manager. Orientation is fun, but isn't what the company is really about. (Only the history of the company.) They will issue you shirts and aprons, but it's up to you to find pants and shoes. Some of the things not covered well enough are the 401k plan, medical benefits.
Behavioral Interview with questions on how you would behave in a team environment, and stressful or otherwise adverse conditions. They will also analyze how you align with the company's value system.
Interview questions [1]
Question 1
Tell me about a time when you had a conflict with a co-worker.
Manager wanting to hear about you, your skills and basic knowledge. Showing respect and enthusiasm. Basic, getting to know the company, a friendly environment and the challenges it may come with.
It was a hiring event so about ten people were doing interviews all at once. They had several store managers doing the interviews. I had a district manager interview me.