The first action your dentist will take will always be to drain the abscess. Following this, the treatment depends on the cause and damage:
- For an abscess caused by gum disease – root planning and scaling and antibiotics
- For infected pulp – root canal surgery
- For damaged tooth/teeth – extraction and replacement
“A dental abscess can be very painful and should be evaluated by a dentist as soon as possible."
The treatment options are discussed in this article: https://yourdentalhealthresource.com/what-is-a-dental-abscess-and-how-is-it-treated/