Some concrete suggestions, in order of likelihood to work:
Meeting people through mutual friends: Probably the best way, the most natural type of social interaction to begin with (as opposed to trying to find a complete stranger to start dating), everyone's relaxed, and you don't have to break the ice nearly as much, can get tricky if you get rejected and have to be around them with friends at a later point though.
Atypical places that are relaxed, non-threatening environments (opposed to bars and the like) where you're likely to see someone by themselves where you can interact/flirt with them one-on-one, without the pressure of other people being around are good, and there's no downside if they reject you, because you probably won't see them again, bookstores, farmers' markets, that sort of thing.
People at work/classmates are a bit more difficult to make the first move with than mutual friends, because it's a more formal social setting. and you have to deal with office gossip in the case of offices, especially if you get rejected.
Probably depends on the area you live in, but usually single people at bars/clubs nowadays are just looking for a one-night stand, so not really the best place to find "girlfriend" material. Actually, the whole bar scene is more trouble than it's worth, usually you're not meeting people one-on-one, they are there with their friends, and that's not necessarily a good dynamic to begin with, e.g. people might pretend to flirt with you if they notice you're a bit "off" body-language-wise because their friends get a laugh out of it, etc.
Online dating: Avoid it; you're just scraping the bottom of the barrel, although that might be good for "practice dates" with people you're not really that attracted to, if you can find a few. It's awkward to back out of those situations sometimes, but the online dating culture is such that it's easy to blow people off, because you're essentially on an anonymous blind date, if you only give them your first name (and you could even make one up, if you really don't want them to know who you are, but that's a bit overkill).
It's really a numbers game, so you have to get out there, which is easier said than done. Also, it's easier to be more social the more disposable income you have.