First off, realize that ATOT is not the greatest place to be asking for advice on women. Seriously, it's like asking for hardware advice on bodybuilder.com (coincidentally, that site is also a poor place to get YAGT advice, but it's probably better than here). You might get a few decent nuggets, but it's primarily going to be stupid pickup lines or advice from keyboard jockeys who have never actually practiced the advice theyre giving out.
Disclaimer aside, there are two main ways to start a conversation:
a) situational opener
b) pre-rehearsed opener
In a situational opener, you have to be witty and think of something on the fly in your given situation. The problem with this is that you have to be witty and you cant make a comment about something retardedly obvious. If she has a huge tattoo on her arm, for example, don't go "hey nice tattoo where'd you get it?" That's not situational, that's lame ass super dork. A girl i met last week in a bar told me yesterday that she HATES when guys do that because its just an excuse to talk to them and its SO transparent. Situational is when she stumbles slightly as she's walking to her seat next to yours in a busy classroom and you say "Dont worry NO ONE saw that. *smile* You must be a ballerina?" Again, this relies on both the situation and your ability to come up with something appropriate.
In a prerehearsed opener you have a few openers that you have available to you at all times. You've prepared for this scenario so you've rehearsed it and know what to say. If you see a hot girl and want to talk to her you automatically have something to talk about. No need to be witty on the spot. Good backup plan.
For example, say a girl is sitting down in the library studying.
You could go direct and show your interest right away: "hi, saw you from over there and knew i'd kick myself later if i didnt say hi. *smile* I'm (john). *shake hands*" Or you could go semi direct and just be the friendly social guy. "hi you seem friendly. I'm new here. My name's John." If she's in a group (especially if the group contains guys), approach the entire group. "hey guys you seem cool. I'm new here, my name's John."
Thing is, when you approach people in general, they normally expect you to lead the conversation initially. Unless theyre unusually friendly or the girl is attracted to you or they recognize you, they won't have much to say. You're some random stranger who's approached them. Think of if some random person approached you and your friends. You'd be like "umm...ok...what does he want?" So you must attract the group. In other words, you must demonstrate some sort of value to them. Yes, you're on a stage. If you have stage fright, you better get over it quick and learn to talk, talk, talk.
And beware of just asking her (or them) a ton of questions. Questions aren't inherently bad but they don't give value. They generally take it. Think of your conversations with your friends. 90% of those conversations consist of you both making STATEMENTS, not asking each other questions. If she's not attracted to you, she won't want to answer your questions anyway, so it's a moot point. It's much easier to demonstrate value by making statements.
What is value? Being interesting. Being funny. Being a cool guy. Being well-connected. Etc. You know all those weird, obscure facts we know as geeks? Those things are interesting a lot of times. Use that. Well, don't be like "did you know that a kilobyte is *actually* 1024 bytes and not 1000 bytes? Because its in binary which means it goes by powers of 2..." But use the actual interesting tidbits we all know.
Take last week. I'm in an elevator going down from the 22nd floor of my friend's condo. Hot girl gets on. The moment she steps in i say something. Because nothing's weirder than the guy who sits there silent and gathers up his courage to say something and then is so nervous that he stutters. "Good morning". "Good morning" she says. Door closes.
Me: *smiling* "Every time i'm in an elevator i'm reminded of the elevator trick. Did you know that there's a code to prevent the elevator from stopping on any floor on our way down?"
Her: "are you serious?"
Me: "Yeah, it totally pisses people off though. When you press your floor, hold the door-close-button while you do it and it'll skip all the people waiting on the way. When i lived in manhattan with my friend Julie we were on the top floor and she hated waiting for a half hour to get to the bottom with all the stops so sometimes when she was in a rush she'd do that and go straight to the lobby."
Her: Haha that's cool. So you're from manhattan?
*conversation started*
There's much more to approaching random strangers than simply having the balls to do so, though that is a prerequisite. Approaching is only the first piece of the puzzle. If she doesn't automatically think youre amazingly cool and handsome, you're going to have to demonstrate your first-rate personality. You DO have one of those, right? If not, that's the first thing to work on. But most of us are at least a LITTLE interesting. We just dont know how to demonstrate it. But the more you approach and the more social interactions you have, the better you'll get at it. And the better you get at it, the more success you'll have and the more confidence you'll gain from that success. It's a spiraling upward process.
So tomorrow, go approach 10 women. You might fail at all ten of them. Big deal. Maybe you'll make a friend or two. Maybe she'll introduce you to other women. Who knows? But even if none of that happens, you'll be 10 approaches more experienced than you are today. So when that perfect girl *does* come along, you won't be sitting there going 'uhh ive never done this before i hope i dont screw it up.'
Good luck.
PM me if you need help.
"Dont wait til youre thirsty to dig a well"
-Chinese proverb