Honeslty, while dwightsteel has a lot of good points, if you're asking about pickup lines, it's an easy conclusion to come to that you might be lacking a little bit in the confidence department.
And the thing is? That is the absolutely most crucial thing for you to have: not because you're not afraid-- any young dude who sees a really hot girl and tries to approach her is going to have his heart pounding like a jackhammer, while the sweat pours like buckets from his armpits. That's called being human.
The trick is to get comfortable with one fact: you are going to get rejected. Accept it. Because once you do, you won't let it prevent you from even trying (and of course, if you don't even try, you're
always going to fail.) The good news is that 99% of the time, the woman will let you down easy tho. Usually by disengaging from converstation, or physically moving away. Sometimes, if they are socially inept (and yes, women can in fact be as big of social retards as guys-- even geeks), they'll be a bit more abrupt, mentioning that they have a boyfriend, or that they're not interested. Then you graciously apologize and then move along. If they're out and out insulting (and it does happen sometimes), you can simply look at them and say "Nevermind then. I certainly wouldn't be interested in someone as rude as you."
Now, some things that will help stack the deck in your favor.
The inital assessment: Do a little surveilance. Watch who she is interacting with. Is she with a guy? With a bunch of friends? What are the pairings like? (i.e.- does it look like she's with a group of couples) Is she alone? How comfortable does she look? Is she fidgeting a lot? Checking her watch/phone?
But for god's sake, don't stare. Stay involved in your conversation with your buddies, and just keep an eye out. You can and probably should make a 'fly-by', where you pass near her. Use it to glance at her and see if she sees and acknowledges your presence, and if she smiles. (If she doesn't, it's not a no-go, but if she does, it's a good sign. Smile back, ya prat!)
Opening strategy: Sometimes, the hardest part is figuring out how to start the interaction. If you're at a bar or a party, and you notice her drink is getting towards empty (or she doesn't have one at all), the "Hi, can I get you (another) drink?" actually works fairly well. It's nice because it has the built in failsafe of allowing them to say "no thank you, my boyfriend is getting me a drink", so you know you're not wasting your time. Failing that, your best bet is usually to observe and try find a comfortable topic. If worse comes to worst, you can probably use the old standby of "How are you doing this evening?" It comes off more sincere than the "nice weather", "come here often" or whatever.
the conversation: this is where you're really going to have to work hard. You need to inquire, observe, process, and then use information very rapidly. Once you open the conversation, you should parlay it into something that is relevant and then try to point it into the realm where she is talking about herself. An example would be "Do you like movies? Have you seen {current release} yet?" She says 'yes', you can ask if she liked it, and if she did, what about it she liked-- is she a fan of the genre, etc., or if she says 'no', you can turn it around and say 'seen anything good?', which you then parlay into a discussion about genres etc. You can also try music as an opening subject. I never did because I like some pretty obscure bands, so it usually ends up being a conversational dead end, because I can't really talk about pop, rap, hip-hop, etc. But of course, if you're at a concert, I think it might be safe to assume that music is a good topic...
During this whole process, it's vitally important to keep observing and using the information you gather. Is she looking distracted, fidgeting, glancing about, etc.? You're either losing her interest or already lost it, if you can't shift topics to something that will engage her again, you probably should cut your losses and get out. You can still try to get her number (after all, maybe it's really not you that's causing her to be distracted), but I doubt that conversation is going to go very far, at least not right then. Is she making eye contact, has an open posture and positive body language? Then you're on the right track.
Normally, you'll find it somewhere in between, but you'll get better at the process as well as figuring out what to do next as you get more practice.
A couple of final thoughts:
1) if you have a female friend or sib who is close to you in age and you trust them, try a little role-play with them. Honestly, the best way to try to understand women and how to meet them is to have 'a spy in the enemy camp', so to speak.
2) when you are going out and you intend to look for girls, make sure you are clean and neat. Not saying you have to dress up, but whatever you are wearing needs to be clean, non-stinky, and generally wrinkle-free. Slobs' chance for success approaches zero. Also, make sure your brush your teeth, your fingernails are clean, your hair isn't greasy, and you don't smell like a french whorehouse (i.e.- don't bathe in cologne. Yes, Oh-Em-Gee, the Axe ads are wrong!) I have had much more success with just smelling like soap and shampoo than I have had wearing the most expensive cologne.
But if that was TL
R for you, just take the first point: be confident and prepare to be rejected, often, and you won't find your fear preventing you from even trying.
I still say, your best bet, and the best way to stack the cards in your favor, is to get involved in social activities that involve your interests. That way, you have a built-in conversational subject to broach with any girl who is there than you might want to talk to.