It's a little tough to find cocktails anywhere. Mainly you'll find beer and Soju, which is a rice drink, not beer and not wine. It's pretty good, but the whole table usually orders one bottle and drinks it from tiny tiny shot glasses. The etiquette for Korean drinking is pretty funny. You can never pour yourself alcohol. Somebody has to pour yours for you, and you need to keep your eyes on peoples' glasses so that when they are empty you promptly fill them. Of course this means you have to hope that somebody is watching your glass too.
When somebody is pouring your drink, you hold your tiny shot glass with one hand, and place your other hand either on the underside of the glass, or on your other wrist. It's polite or something to receive with both hands.
If your glass is empty and nobody notices (and you're Korean), you say (in Korean) to the person next to you: "Are you busy?" And that's a clue that you need more alcohol.
If you're American, I found that usually if you tap tap tap your glass on the table for a while, somebody will get the hint eventually.