What's the best method to heal nerve damage in my wrist (puncture wound)?

Did it cut the nerve: If so go see hand surgeon asap.

Nerve damage. : If the puncture cut the nerve it may mend itself but this is rare. Surgery will be required to repair the nerve. If the nerve is only partially injured it may heal itself. I would make an appointment with a hand surgeon.

Needs fixing: If you have nerve damage fro a puncture wound you have at least a partial laceration of the nerve. You need to see a hand surgeon to get the appropriate diagnosis and probable surgical repair whe it is fixable.