How can you relieve gum ache?

It depends: This depends on the cause of the aching gums. It may be food or tartar trapped around or beneath the gums. It may be a lesion or ulcer. It may be an infection of the gum or tooth. A diagnosis by a professional will help you determine the appropriate treatment.

Treat the source: Treat the cause, not the symptom. Gum ache can be relieved by taking drug (tylenol, motrin, or Ibuprofen with warm water), gum massage with gentle brushing in the area, or any attempt to reduce the inflammation by establishing drainage. The real trick is to treat the underlying cause such as periodontal disease or endodontal abcess, area of food impaction, malocclusion, etc. See your dentist.