There is no button that will make your character sprint, but there are a few simple ways to increase the speed at which your character runs. Pushing forward on whatever controller you use will make your character walk forward. Here is what you can do to make your character run faster in Fallout 3.
Holster Your Weapon
If you put your weapon away you will free up your arms to be able to focus on running. Holding down the button you use to reload is usually the way to holster your weapon. Once the weapon is gone you should immediately run faster.
Equip Light Armor
Lighter armor lets you run faster. The reason why is fairly obvious when you think of how it would work in real life. The less weight on your body the faster you will be able to run.
The higher your agility is, the faster that you will be able to run. This is a tough one to really do much about as SPECIAL points are far and few between, but if you hate running slow, then throw a few points toward increasing your agility.