I fractured a bone in my hand. What are some exercises I can do to make it stronger faster?

None. Exercises are for muscles. Normal, unbroken bones benefit from exercise in that stressing the bone forces it to constantly remodel itself, thus keeping itself strong. But you have a broken bone, and it needs to heal. That doesn't mean you can't exercise; a physical therapist can give you gentle exercises for the surrounding muscles that will keep them strong while allowing the bone to heal.
Motion first then... Once your symptoms start to improve, you should start trying to increase your motion, but gently. Increase the motion as tolerated. Once you have regained functional motion (able to do most activities) then start strengthening exercises to improve grasp and pinch. Wrist flexion extension exercises with light weight should be initiated last.