There are two ways you can get a tooth abscess.
The first way is with is an infection inside, in the living pulp tissue. You either get tooth decay or severe irritation of the inside. Ordinarily, when you have an infection, your body responds by sending white blood cells and antibodies to kill the bacteria. The tissue will then swell and turn red. However, there is no room inside your tooth for the tissue to swell. Thus, this natural defense mechanism breaks down. Antibiotics will not stop an infection inside your tooth. So, unless you address the decay or the tooth irritation in time, the pulp tissue of the tooth will die and the infection begins to spread into the surrounding bone.
This is what is called a tooth abscess. It can cause a painful toothache, it can cause the tooth to be just tender to pressure, or sometimes you won't even notice it. Once the infection is in the bone, your body can fight it. Depending on how aggressive the bacteria are, your body may be able to wall them off and you can live for years with a tooth abscess.
The best way to treat it is with a root canal treatment. Click the link to learn more about root canal treatment. We have a number of pages of information that you can read about this.
Some people prefer tooth extraction thinking it is easier. But not only does a missing tooth lead to possibly serious jaw problems and damage of other teeth, but it is the most traumatic type of dental appointment I know about.
The second way is that you can have a gum infection. This can come either because of gum disease or an impacted wisdom tooth or other impacted tooth. Since this isn't inside the tooth, your body defenses will be at work. Treatment of the gum infection would involve a thorough cleaning of the root surfaces and other procedures to fight gum disease. There are specialists called periodontists that have advanced training in the treatment of gum disease.
Or, in the case of impaction, the treatment would be wisdom teeth removal.
Click here to read about oral yeast infection.
Click here to read about why a dead tooth isn't really dead.