The same way you deal with them every other day of the year. Listen, I know it can be annoying having a drunk person spitting all over you, and all the other unpleasantries that come with someone who has had one too many, but if you're going out to celebrate the new year, then focus on that. Have fun! Let the drunks be merry, and you be as far from them as possible should they feel the need to get sick.
And if you don't normally go out, because you don't like to be around drinkers and New Years is the exception, than just be understanding that people all have fun in their own way.
Hey, at least you won't have a hangover.
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