Wear a decent shirt and some nice jeans or slacks, and make sure you look well groomed and presentable. Walk into a place of business that you'd like to work at and ask if a manager is available. Since you have no work experience you'll probably need to sell yourself to them in person instead of just mailing or dropping of and application
If manager is available introduce yourself, shake his hand and look him in the eye. Say "I'm looking for some part time work and was interested to know if you are hiring now or are going to be hiring in the near future" He'll say yes/no or we're accepting applications. If he says yes, asked for what position are they hiring for and also ask to get an application. Now this is important....... don't just run off as soon as he hands you the application...... instead ask about the position available (days and hrs you'd be working) and also maybe some other stuff you might be interested about.
If it sounds like the job will be a good fit for you, start to sell yourself. Say stuff like "I have a good work ethic" "I'm a strait A student" "I'm dependable and I always show up to places that I'm supposed to be at" and etc
Near the end of selling yourself don't be afraid to ask for an interview. Be like "I'll fill out this application and do you think you'd be able to schedule an interview for this week or next"
For those beginner, part-time jobs you just need to separate yourself from the rest of the applicants and you can easily do that just by dressing decently, being friendly and talkative, and showing your actually interested in working there.
I can't tell you how many times some guy has just walked up to me looking like he just rolled out bed, handed me an application, and just left barely even introducing himself or shaking my hand or even acting remotely interested in what he was doing.
If a guy walks in and ask for a member of management and presents himself (heck a freaking, smile and hello how are you doing today? My name is Jim Bob and I'd like to apply for some part-time work) and I'd likely hire him on the spot.
Also don't be afraid of fast food places....... really high turn over and you can move up to management in about 6months or less if you have a good work ethic.