Just... go. There's no secret or anything. Things WILL start off awkward, almost always anyways, you just have to power through it. Talk. Talk about stuff, about life, deep stuff, shallow stuff, fun serious, music, interests, etc. but most importantly: ENGAGE YOUR DATE, make them talk too, make sure they have fun, and they'll do the same in return, it's all about give and take.
To address what else I see here: don't worry about alcohol, drink however much, or little, you like.
EDIT: Haha, I thought this was about going ON a date. In terms of pursuing a relationship:
Listen... It's all the same, on a dating site, in a bar, a stranger walking by you. Yes, you can meet someone amazing online. There's no debate that you WILL meet people, just remember that you can meet someone anywhere. Be aggressive, you don't have to walk straight up to them and boldly declare your love for them, but you can and SHOULD ask them out if you feel like it. It can be a simple as sending them a message on Facebook.
DOUBLE EDIT: Go anywhere and make friends. Or just acquaint yourself with people. It can also be online. It's not as weird as you think; Heck, if someone I knew online asked me on a date i'd go (provided i've actually seen them before).
There are dating sites and then there are "dating sites", make sure you choose the right one.
... Also remember that the best relationships are between best friends.