Confirm that this is the problem. X-rays are usually needed to show exactly what the problem is. Treatment really depends on the type of break. Again, it really depends on what the break is. The biggest problem people have after a finger fracture is stiffness.
Stiffness means difficulty bending or straightening finger joints.
This is very common, and is more likely the closer the break is to where the finger meets the hand. The best way to prevent stiffness is to move joints as soon as possible. Sometimes the break is too unstable to let the fingers move - even with surgery, but otherwise, it's best to start moving the fingers as soon as possible. It's a roll of the dice. You may luck out and wind up with a pretty good result.