Ok. The whole sentence is:
Person A bandages Person B's arm.
Person B says: ありがとう。ずいぶん慣れた処置ね？看護婦でもやってたの？
I get what the sentences are saying.
But! For the life of me I can't parse ずいぶん慣れた処置ね？ into that makes any sense to me. All I can come up with is: "You do very accustomed treatments." Which I know barely makes any sense (grammatical or otherwise).
Can someone please break this down for me?
慣れる can also mean "become skilled at", so it's more like "You've become quite skilled at this treatment. Were you a nurse or something?" More literally, it would be like "This is a treatment at which you've become quite skilled." There is a です that's omitted before ね？; if this wasn't obvious to you, that may be the reason you had trouble with it. So there's no "do" in it as you were thinking. It's an "is".
ずいぶん 'very' is an adverb and an intensifier modifying 慣れた 'became accustomed'. ずいぶん慣れた is a relative clause modifying 処置 'treatment'. ずいぶん慣れた処置 is a nominal predicate. Here, its subject is omitted. The copula だ is optionally omitted before certain elements including the sentence-final particle ね. To reconstruct what is omitted, it would be like this:
(あなたの処置は)ずいぶん慣れた処置(だ)ね。
'(Your treatment) (is) a very accustomed treatment, isn't it?'
I don't have much to add to the already posted answers, except you might be interested in knowing that omitting the だ before ね is mostly female language, and would rarely be used by males.
Of course, this distinction only applies after nouns and na-adjective stems, since verbs and i-adjectives don't have a だ to begin with.
Another sentence ender that this phenomenon occurs for is よ:
好きよ！ I like/love you! (mainly female)
