I had all four of mine removed when I was 16 (on New Year's Eve

) before they even grew because I didn't have enough room in my mouth for them (and my parents weren't about to have that $5,000 they spent on my braces go down the toilet.)
I don't know how they do it when your teeth are already grown, but they had to open my gums up, break the teeth and yank them out.

Despite all that, recovery wasn't all that bad. They gave me vicodin for pain but that honestly made it worse (it made me really dizzy, sleepy, nauseous, and all around drugged.) I slept lots and watched Disney movies all day and I was on my feet and feeling pretty good less then two days later. Thank God I love soup and pudding though, because that's all I ate for like a week until my stitches dissolved.
ETA: Good luck! I'm sure you will be ok. I have really sensitive teeth and am really bad with dentist drills and needles also. I'm sure if you voice your concerns to your dentist he/she will hopefully make it as smooth and painless of a procedure as possible