There's lots of great advice in this thread about location, and tips on how not to freak someone else out.
But one thing to keep in mind, probably tip number 1 in my mind anyways, is once you've met someone interesting, don't forget to pull the trigger.
By this, I mean you have to act if you want to get anywhere. Don't worry too much about the consequences of said actions, and play it relaxed. So, if you see a lady you might be interested in, strike up a conversation. See if you can get 5 minutes of not-uncomfortable small talk. If you can get that far, maybe ask if she'd like to continue the conversation over coffee. Don't suggest coffee at a later date (but don't argue if that's what she counters with) -- just do it.
Commit yourself to coffee and nothing more. Do your best to convince yourself that the entire meeting ends once the cup is empty, and just focus on having a meaningful encounter for 20 or 30 minutes.
If things are going well, hint that it would be fun to meet up again sometime. If she agrees, ask for her number.
When you call her back, have something interesting that you'd like to suggest doing. Dinner is always safe, but make sure the restaurant matches the girl (eg. if during coffee she mentioned that she moved from the coast to Wisconsin, and misses Indian food, see if you can find somewhere with a wicked curry - don't, however, just book a dinner at a nice restaurant and assume that's OK). Better than dinner, try finding an activity, with a fixed start and stop time, that could be fun for both of you. Maybe there's a con or a concert in the park, or you and some friends are heading to the beach for an afternoon with a bar-b-q (note: this is only a good idea if there are other ladies coming, four dudes on an empty beach will be creepy).
If you think things are going well, and you feel a spark, initiate some kind of physical encounter. Start with casual touch (putting your hand on her shoulder, or on the small of her back), then move up to less casual from there. The more basic contact there is, the less creepy non-standard contact will seem. That is, if you kiss someone out of nowhere it will feel strange. If you have already been in physical contact, it's the next logical step. Also, this gives you a good way to assess how she's feeling. If she recoils in terror, you're probably not getting lucky tonight. If she's fine with it, or if she seems into it, awesome. Then, by all means, man up and kiss her when the time seems good. (But don't' wait too long or she'll get confused and think that you're her new gay knitting friend. You have intentions, let her know them.) A lot of geeks fool themselves into not acting on the physical side, by saying things like 'I'm respecting her boundaries by letting her pick the level of physicality...' Blah blah blah, most (not all) women are taught to not initiate things like a first kiss - they are supposed to flirt and encourage you to act, but not to actually do it. If you don't, you'll both end up waiting.
At this point, I leave the rest up to you.
OK, so this seems like pretty basic advice, but all of this is a specific counter to something that would block your standard socially awkward introvert:
- Not starting a conversation. (Just talk to her!)
- Not asking for a date. (Coffee is a date, but isn't scary.)
- Putting too much pressure on the first date. (You're just meeting someone, not assessing their potential as a life partner)
- Not calling her back. (Why do people ask for numbers they won't use?)
- Being over the top, or too generic in the second date. (Pick specific, interesting, encounters. And yes, your selection is a test.)
- Scared of physical encounter. (Touching is good.)
- Not getting past the friend barrier. (Once you are kissing someone, they have a good idea of where the relationship is going.)