If they've erupted, your general dentist can remove them; it should be pretty uncomplicated and the recovery just like any tooth extraction.
If they haven't erupted it's more complicated and you'll have it done by an oral and maxillofacial surgeon. 2 of my kids have had it done in the last couple of years and it hasn't been bad. General anesthesia was great, my son required one dose of vicodin when we got home and then switched to Motrin for a couple of days. My daughter, the Queen of Drama, had more pain, was very miserable for the first 24 hours then did fine with the Motrin. The swelling is always worse the next day, I think it's very beneficial to do the alternating warm/cold packs as instructed and to take it easy for a day to avoid any complications.
Most of the experiences I've heard of these days have been straightforward and uneventful. Quite different from my experience 20 years ago in college, where I hooked up with an ER resident and his dental student wife and had a "free" extraction of 4 impacted wisdom teeth in their garage with a stolen tank of nitrous oxide......