How long will a tooth infection take to heal once its been extracted?

Healing..... It depends upon many factors including but not limited to your age, healing ability, general health, size and location of infection, duration of infection, type of bacteria involved, blood supply in region, etc. Antibiotics should also be prescribed. You may begin to feel better within a day or so, although complete healing and bone remodeling may take weeks or even months.
Several days . Usually after and extraction, the infection will clear up rather quickly. The extraction allows an opening or path to drain the infection and the body responds quickly to clean up the mess.