Well, you can do it two ways. You can let them put you to sleep or you can stay awake.
You recover faster if you stay awake (which is what I did) so I can tell you about that way (it also costs like $400 cheaper).
The operation occurs in two steps. First, the dentist takes a small needle and injects a numbing chemical into your gums which 'freezes' your gums so that you can't feel anything. It's a weird feeling and it's unpleasent when they have that needle in there. But, it feels uncomfortable and weird more than painful.
Then the dentist will come back after 10 or 15 minutes, allowing the freezing to reach maximum potency. Then s/he take something that looks a lot like a screw driver and they push down in the middle of each of your wisdom teeth to 'crack' them. That breaks their roots and they just pull them out.
Then you're given a bunch of gauzz and stuff to stick in your drooling bleeding mouth. Which is totally gross the day after. Oh, and you get a little plasic syringe thing to shoot water into the holes after you eat to dislodge food that will get stuck in there.
The next day you should be okay. But, it will take a long time before those holes close up and you don't get food stuck in there anymore. That's the worst part.