I finally figured out what was bothering me about the phrase "plastic surgery". For whatever reason, you don't hear it much anymore -- for people who really need it, it's more common to say either "reconstructive surgery" or be specific about what is being "repaired" (cleft palate, mastectomy replacement, etc.). Otherwise it's referred to as "cosmetic surgery" for procedures which are voluntary and serve entirely to enhance someone's appearance.
Officially it's still called "Plastic Surgery", but I suspect many plastic surgeons who do reconstructive work want to distinguish themselves from those who do only cosmetic work, and so don't like to call themselves "plastic surgeons". Instead they'll list their accomplishments with people who have congenital defects, or burn victims, or other disfigurements that prevent them from leading full, healthy lives.
Anyway, while "cosmetic surgery" is a more "formal" term used on television and in advertising and medical journals and so on, a common way to express this in casual conversation is, "He/she has had work done". This doesn't apply to just facial surgery, but any kind of cosmetic work.
If you want to be specific to the face, it depends on the kind of surgery. You might say "he/she got a lift" (short for "face lift"), or "she's had some Botox". Or you can just say someone had a part of their face "done":
She had her nose done yesterday, so she's staying inside until the swelling goes down.
For certain surgeries, you can say "a nose-job" or "a boob-job". Sometimes people get "an injection" which usually means collagen to make the facial part look (temporarily) larger and more sensual. Lips are common, but also cheeks and other parts of the face.