Yes and no. I used to manage a retail store that hired young kids. You need a written something. Put your name and phone number at the top. Write like "objective: looking for my first part time job... Skills: good interpersonal skills, team player, fast learner... Other: insert ANYThiNG you have here - soccer team, babysitting, Coldplay fan club, etc".

Just put these things in a point form list. But yes, ask if they're hiring they will usually give you an application; fill that out and attach your "resume". If comfortable, ask to speak to the manager directly. This is where you sell yourself. Just be clean and polite and not shy. Tell them exactly what you want; that you're looking for a couple of after school/weekend shifts. You'll be fine! I suggest you try the grocery store first.