Fairly simple, just be transparent and be as flexible as you can. When I applied, I was starting college, and I had no previous job experience. Can't speak for all Publix's, but will train, just don't expect them to hold your hand, and they will let you fend for yourself.
I applied in-person. I interviewed at Publix (Atlanta, GA) in Oct 2012
Interview
Manager told me to come in he would just hire me no interview necessary. The girl filled out my paper work then told me I would get 9 hr and more on my first review the manager would bump it up. 2 weeks later no call, I called back and the girl forgot to put my information in the computer, two weeks later then they hired me. And gave my job to someone else.
I applied online. The process took 2 weeks. I interviewed at Publix (Atlanta, GA)
Interview
one interview with a store manager and a department manager. More of just a vibes interview especially if your in high school/college. just dress professional and don't be weird. also have an answer for basic questions like "why do you want to work for Publix"
Very easy. Simple questions and basic interview questions. Nothing tricky. Just call back to follow up since the managers seem to forget to call sometimes. There is only one interview process before they call and let you know.