Public court? That's so awesome to have, never in a thousand years you'll see something like that in my country. Where are you from?
As Clear said, just hit the ball. It'll eventually come around. I could give you a couple of tips though.
* Check your racquet. If the handle and the head are not the same 'structure', meaning they're attached together, you should consider an upgrade ASAP. Used pro racquets from previous seasons (03'-07') are disgustingly cheap and it will mean a world of difference.
* Youtube videos. It may sound cheap, but there are some great tutorial videos that will lay out the basics for you. You can practice motions/balance at home and then practice in court.
* Stiff wrist-elbow-shoulder-waist is a nono. Don't be afraid to lose that wrist! I can't stress that enough. It might make you more insecure, but it's the way to go. After a couple of hundred strokes your swing will get better and better and lots of balls that would otherwise go wide or long will start landing in court.
Looking forward to hear from you in the future. Keep at it!