I applied in-person. The process took 6 days. I interviewed at Publix (Miami, FL) in Jan 2015
Interview
I called the manager on a Monday and was told that she didn't have any positions. However, she asked for my name & number in case anything came up. I applied the day after anyways, and then I got a call from her on that Friday asking for me to come for an interview. Interview was pretty brief and easy, it was just basic questions, nothing to hard. And she was very welcoming!