Although I don't know your age, school or job status, and what you intend to do with the money, I'll give you some basic tips on getting what you want.
How do I convince my parents to give me ten bucks?
First, remember that every negotiation in life is a give and take. To get, you have to give along the way. If you pitch in at home, try hard to do well in your studies, and respect the people around you, you're in a much better position to make a request than if you see yourself as the center of the universe.
If you're hoping to have Mom and Dad hand over ten bucks, be prepared to explain why you need or want the cash. Whether you want to buy double desserts at lunchtime or take in a weekend movie, your job is to be honest when you ask. If, for example, you say you want to pick up some new folders from the bookstore and you decide instead to drop the change in vending machines, expect the gap in truth to widen into a gap in trust.
When you approach your parents, consider their position. They may not be able to spare you the extra dollars, especially if they have other family members to care for. They may also suggest that you do yard work, scrub the bathroom, or babysit with your siblings to earn the extra cash.
Importantly, accept your parent's decision. Getting angry, whining, or pouting may gain you some attention this time around, but you won't win any points for your next negotiation.