Doesn't need to be a general anaesthetic
@creaky, I had all four impacted wisdom teeth pulled with twilight sedation about 20 years ago - you're kept on the edge of consciousness by the anaesthetist. I remember having a moment of lucidity during the procedure where it felt like the surgeon was going at me with a pair of multigrips as I felt my head being flung from side to side, but they must have given me a quick squirt of juice and I was out again in an instant.
Post-procedure, you can expect some pain. The severity will probably depend on how much they have to bash around inside your mouth getting your teeth out. Take whatever they offer when you wake up and lie about how much it hurts on the 1-10 scale when they ask, particularly if Fentanyl is available - who doesn't want medical grade heroin! You will have open sockets in your jaws where the teeth were, which can get infected, and will probably be told to rinse with warm salty water after eating for a while to help keep things sterile while you're healing. One of my sockets got infected and it felt like a bad toothache. Fortunately I had follow-up appointment with the surgeon that I managed to bring forward because I was in pain, and he packed the hole with some sort of clove-poultice. Cloves apparently have antiseptic properties and within a day or so, the pain was gone.
Dental work these days is nowhere near as bad as it was 40 years ago; better methods and local anaesthetics make it a lot more bearable. Like
@cammas, I've also had a crown installed (largely due to something a dickhead dentist did many years earlier, destroying a tooth) and was a simple and relatively painless procedure.