What is the best method (diet or therapy) to heal nerve damage from a puncture wound in my wrist?

Nerve repair. If a nerve has been cut or even partially cut it will not heal on its own. You need to have the nerve repaired. If the nerve has been traumatized or crushed it might or might not heal on its own. See a hand surgeon.
Nerves heal w time. Nerve damage will heal unless nerve is severed or irreversibley damaged (axonal death) where the thumb wont oppose the little finger. It will otherwise return at rate of one inch per month. To facilitate this avoid pressure on area of damage (splint). Otherwise acitvity is okay. B12 has some neuropathic effect, but only if there is a deficiency and Folic Acid at 800 mcg daily couldn't hurt.