You didn't even say what surgery you are getting, are you talking about getting your wisdom teeth pulled? How would we know what kind of anesthetic they are going to use? Why not ask them? Several methods of anesthesia are available, which method of anesthesia is used is chosen by you or your dentil/oral surgeon depending upon the nature of the surgical procedure, the risks and benefits of each method, and your level of anxiety about it. Many people get wisdom teeth removed with just a local anesthetic (numbs just the area), like what they use for other dental work. Sometimes they might give you a sedative/ anxiolytic/ amnesiac (makes you not remember). Another option is to have a mixture of nitrous oxide and oxygen is administered; you may remain conscious but relaxed/sleepy and kind of "out of it", and you still get the local anesthetic as well. Then there is also the option of IV sedation/general anesthesia. If you are extremely anxious about having your wisdom teeth removed you should have the option to choose intravenous anesthesia. You should really have talked to your dentist about this beforehand - we can't know which one they've chosen for you.
As for level of pain, that totally varies depending on the person, what anesthesia is used and how effective it it. Pain afterwards varies greatly from person to person too.