This is all to say that New Yorkers are historically fantastic about dealing with celebrities. Not that we don’t have our invasive moments, or gush about “celebrity sightings” when they’re over, but in general the rule is to treat a celebrity like you would any other person on the street/in a restaurant/at the grocery store. Don’t stare, don’t start talking about them, don’t yell “oh my god you’re Lucy Liu!” when they’re walking down the street.
If you’re a huge fan, you may be inclined to ask for an autograph or a photo. This is one of those things that seemingly comes with the territory of being a celebrity, but this is when common sense really needs to go into overdrive. Is the person in question at lunch or generally engaged with something or someone else? Then, like anyone else, they would probably rather not be bothered. If Helen Hunt is casually browsing books at a bookstore perhaps you can go up to her and say you’re a fan, but you should not if you see her in a restaurant eating with her family. Bill Murray always seems game though.
However, there is a catch to the “just treat celebrities like normal people” thing, which is if you are a total weirdo around people it might come off bad around celebrities. Here’s an example: A few years ago my fiance and I were at a fancy, “speakeasy”-style cocktail bar, and both on our third or fourth drinks (which were very strong), when who should walk in and sit down next to us but Zac Efron. He was there with another guy, and was wearing this tight thermal shirt, and I was never attracted to Zac Efron and had never seen High School Musical but holy hell was this man attractive. Just, arms. I was totally star struck, but also determined to keep my cool and not act like he was any different than any other insanely hot person sitting next to me. So I keep chatting with my fiance, when I hear Zac Efron order a drink I had. I whip around and say (let’s be honest, I probably yell) “Oh my god, I LOVE that drink” as I reach over and grab his bicep for friendly emphasis. Like you’d do to maybe any other normal person if you’re feeling flirtatious and casual but should not do to a really famous person! From what I remember, he was very gracious about the whole thing, saying he always gets that drink when he goes to that bar, and asking if we’d ever been before, and us wishing each other good nights as we turned back to our partners.
So, you know, don’t do that.