In my opinion you should submit you resume along with a cover letter and references so they are readily available. You can ask to speak to a manager when delivering and if you get the chance to speak to one find out if they are hiring and make a good impression. Dont call and annoy, they will call you if they want you. The best opportunities come from netowrking. Talk to the people you know and see f they know people etc etc....

Look for signs on stores indicating they are looking to hire. Stop in and be dressed conservatively. Listen to your out going message on your phone. Make sure it is professional sounding, no stupid songs. On your application state what work experience you have even if you never had a job. Babysitting? community service? volunteering? Beef it up but don't lie. Be flexible and say you will work weekends. Don't give up. You may need to submit 60 apps before you get a job.Calling everyday is not helpful but be diplomatic with your parents and thank them for their interest.

The last two answers were pretty on the ball, but I'd just like to add one thing. If you're trying to get a job at a specific store, your chances are low. With no previous experience it'll be hard to make it to the front of the stack of applications they get. Also, your availability is important. At safeway for example, the ideal candidate is willing to start part-time, but is open to any hours throughout the week. Your best bet is just to apply to as many different places as you can.

I get about 50 applications a week, out of those, I usually interview 4-5, on average I hire one.

So if your chances are 1/50, at one store, that can be vastly improved by increasing the quantity of stores you're applying to. I used to apply to about 50 a month when I was jobless. Just keep it up and don't work at Walmart