The vet will put the kitty under fully, take a set of mouth x-rays. The will check down along the bottom of the gum line and see if there are any red, swollen areas (down in that gap way down in their mouth) If there are red pockets of swelling it is highly possible kitty has a case of gingivitis or worse yet, stomatis.
Stomatis is an organism that attacks the teeth in a cats mouth and the only way you can get rid of the pain in the cats mouth is to remove the entire tooth and scrape out the root. If it is not a good dental vet, if he leaves any of the organism in the mouth, it is free to attack other teeth and eventually you have a kitty with no teeth, in a lot of pain and eating gruel for the rest of his life.
If you do have to take kitty to get oral care make sure it is a vet that specializes in dental work.