How do I treat burns to my finger?

Depends... On how large and deep the burn is. In general, a burn that heals in less than three weeks does not need surgery. Initial treatment is to wash with soap and water 1-2 times a day, apply an antibiotic ointment (bacitracin) and a bandaid. Elevate the injured hand above your heart to prevent throbbing and keep moving the injured finger to prevent stiffness--it should gradually heal.