In general I don't drink. (I'll make an exception maybe once a year or so.) I don't like the taste, I don't like the feeling of alcohol affecting me, and I don't have any interest in losing any of my inhibitions. (Also, if I'm going to consume empty calories, I'd prefer something I actually enjoy.)

I order a soda or something (maybe with a twist of lime or lemon--it looks like others' drinks, and also, I like them) and don't make a big deal of it and no one really asks; if asked why I'm not drinking alcohol, saying I don't like it is usually enough. (Though it may be more socially acceptable for women not to drink, too.)

On the rare occasions I do drink, I'll order a glass of water also and take small sips of the alcoholic drink to make it last, while drinking the water for thirst. (Easy enough to do with something I don't so much care for, though I like ciders and sparkling wines well enough.) I have an easier time being more open and extroverted when others around me are, so if others are drinking, usually they won't even notice or care that I'm not. If you're acting while sober like others are while tipsy, it's not as socially awkward.