Long story short, I'm a 20 year old guy, not into neither drinking or partying. As a result of that I've never been in a "real" relationship with a girl. I don't feel comfortable "putting the moves" on someone, and most of the couples I know have gotten to know each other while drinking/partying or through people they have gotten to know on parties.
clubs, your classes, study groups, your work place? Get your friends together and plan adventures ask them to bring along other friends and single girls they know and head to the beach? Contact girls from high school or your past and ask them to hang out sometime? Or maybe even go to parties and pretend to drink its not that hard just stumble everywhere and slur your words a little. plus the girls you want are the smart ones not getting drunk so bonus points if you aren't either. As for not being able to put on the moves just be nice talk normally and expect nothing show interest but don't get worked up about it. be cool girls like cool guys right? just be like "this party sucks want to talk for a little?" If your friends have girls maybe they can help. just don't act hopeless and pathetic unless you want girls running from you.
i must agree with the poster above me. dont have to drink to go to a party, and often enough there is a girl who is in a similar situation. try the other ideas too and good luck!
~Women buy food at the super-market. If you buy food at a super-market you might have a food-related question to ask the woman & a conversation might organically grow. She might ask YOU out.
~Women go to Sporting-events. If you go to Sporting events you might have a sporting-event-related question to ask the woman & you two might score a conversation. She might ask YOU out.