You want rules for a one-armed character?
You suffer a -4 penalty on all Climb checks. You suffer a -2 penalty on all Craft, Disable Device, Escape Artist, Forgery, Heal, Open Lock, Sleight of Hand, Swim, and Use Rope checks. You suffer a -2 penalty on all Strength-based checks. You are unable to wield any two-handed weapons.
These were gleaned from the Variant: Damage to Specific Areas in the DMG. I just applied the penalties for damage to a hand and damage to an arm, doubling the ones that overlapped. However, I removed the penalty to attack rolls (which would have been a -4, since both hand and arm suffer from it, doubling the penalty) since you would be using your other remaining arm.