It depends upon what structures have been damaged.
If you broke a bone, then the fracture needs to be reduced and held (either casting or surgery).
If a joint was dislocated, it needs to be reduced. Then, if it is stable after reduction, it is placed in immobilization for a very short period of time. This is then followed by intensive occupational therapy.
If you tore a ligament, then usually the ligament will need, at least a period of immobilization, followed by therapy. But, if the immobilization does not heal the ligament, then surgery will be needed to sew the ligament ends back together.
If it is just a bad bruise (hematoma, bone bruise), it just needs a little protection, ice, compression wrap, and then therapy.
So, if you think it is more than just a minor contusion (bruise), you should probably have it evaluated by a hand surgeon or orthopedic surgeon, and maybe some screening x-rays.