How long does nerve damage typically take to recover from hand surgery?

Roughly 1mm/day. Peripheral nerves, if cut of severely bruised/crushed, can regrow/regenerate but the rate depends greatly on the age of the patient and the presence of other medical problems. Young, healthy patients typically regenerate ~1mm/day but there is a lot of variability. A lot also depends on the severity of the injury itself.
Nerve Healing. Injured sensory nerves in the hand can regrow in many cases. If the nerve has been bruised, or cut/repaired it will typically regrow from the point of injury at 1mm per day. This rate varies with age - younger is better! You can tell where the point of regrowth is by tapping along the path of the nerve; the point of growth is marked by a small electric shock sensation!