There are three types of anesthesia, and depending upon the nature of your particular procedure coupled with your comfort level, you'll end up receiving it in one of three ways:
Local Anesthesia: Administered by injection at the site of the tooth extraction after using a numbing agent. You'll be awake for the procedure, and though you'll feel some pressure and movement, you shouldn't experience any pain.
Sedation Anesthesia: Administered through an intravenous (IV) line. This sedation type allows you to sleep through the procedure so that you won't feel any pain during the surgery. Your surgeon will also numb your gums.
General Anesthesia: If you're not keen on needles, general anesthesia can be inhaled. Much like sedation, you will be asleep throughout the procedure, and your vitals are all monitored by the surgical team.