I've had wisdom teeth out under local anaesthetic and a hernia operation under general
anaesthetic: this really is stress free, modern anaesthetists are very good. The anaesthetist will come and see you first so you get to know him/her and get put at ease. They put a catheter into the back of your hand through a needle which just feels like a scratch as it goes in, then you can't feel it. First they put something through the catheter to start everything flowing, it just makes your arm feel a bit cold but doesn't hurt. Then they put something which makes you go all chilled out but isn't the proper anaesthetic, while he's talking to you. Then he gradually introduces the anaesthetic until you drift off, but the good thing about intravenous anasthesia as opposed to a gas mask is you don't feel like you are "fighting" against feeling sleepy or anything, you just kind of feel all chilled out and really relaxed and then you don't actually remember drifting away.
When you come round it feels like a Sunday morning lie in, ie you will wake up, look around a bit and think "wahey, its over", and then can't be bothered getting up so nod back off to sleep again for a bit, then wake up again, then nod back off again (this goes on for a few hours so you do get some good sleep). I remember feeling a bit rough, just as though I had had a rough night the night before and couldn't be bothered doing anything other than sleep, but after a bit of extra nap time that goes off.
Now as for having the teeth out, mine were under local, and the main hassle I discovered was that they did bleed for a bit, but it wasn't really painful. Obviously it depends on how complicated the extraction is, if you have upper ones out you won't notice them, lower ones are a bigger job and if they are impacted the dentist will have to work harder to get them out, so it might ache a bit and feel sore although they do give you painkillers for this. The good thing about teeth extractions is your gums have a very good blood supply which means they heal faster than anywhere else in the body. It is difficult to predict how much post operative pain you will have, I literally had no pain, I got the train back home straight after having them out, walked across town, was watching a film that evening and forgot about them. A security guard at the place I worked had his wisdom teeth out and was on painkillers for the rest of the week because they were quite sore.
I'm not sure if you're having them out because they've flared up in the past but, if you have wisdom teeth flaring up because they are infected, thats more painful than having the extraction. I actually had an abscess developing under one of mine when it came out - literally from the day it came out the abscess pain stopped.
Don't worry if you are feeling nervous, its natural to be a bit stressed about the unknown but modern medicine is pretty good and designed not to stress the body - you will more than likely come out of it thinking "hey I could handle that pretty easy"