I applied through an employee referral. The process took 5 days. I interviewed at Hy-Vee (Saint Joseph, MO) in Oct 2012
Interview
Extremely easy to get an interview. If you have a friend that works there, just get them to go talk to HR and recommend you (make sure they're a good worker) and that'll guarantee you an interview. Extremely easy questions and you will likely get it because their turnover is so high since they are employing such young people and they are always hiring.
One interview with HR manager followed by a follow-up drug screen. Overall interview was basic information like employment history, what you are excited for followed by an expectation of hours worked and such.
Emailed me to come in, and then we went over basic interview questions - who are you, why do you want to work here, what are your skills, what are your plans. It's a grocery store, after all
The Hyvee interview process was quick and easy. It was low stress, relaxed, and space was allowed for questions. Hiring manager asked intriguing and important questions that required you to know what they were about and the type of employee they are looking for--a team player.