Actually, a lot of guys I know have this problem. Shyness around women is common if you haven't talked to girls a lot before... But you can gradually get over it.
Just start by waving hello everyday when you see a girl you know, even if it seems stupid or unnatural. Force yourself to smile a winning smile, and 100% of the time you will get a smile back; girls are nice like that. A few days later start saying hi, or hello to everyone you meet. Again, winning smile.
Btw, don't get stoned. But you don't seem like a stoner anyway. ^_^
Continuing... that advice up there about talking to a lot of girls is good advice, the more you get used to having a casual conversation with girls, the less they seem like aliens from another planet and more like people that you can talk to.
Girls that always hang out with their friends are... difficult. .___. I know. If you can, get her phone number (break the ice with a cheesy pickup line or something, but in a joking manner) and ask her for a date, but don't make it sound like you have romantic intentions already... More like "Hey, you wanna go get some Starbucks with me," and less like "Oh Diane, will you please go out with me to dinner?" It is important that as soon as you guys start talking you ask for that date, because otherwise you will get stuck in a girl's dreaded 'friendzone,' which is a real annoying situation (I am in like 10 past crushes' friendzones -_-).
If you get a date, you will probably be alone, unless your girl is a clueless idiot who brought a friend or is jabbering into her phone. Now you guys have some time to talk, get to know each other, etc... Halfway in, ask her to be your girlfriend, do it nicely and honestly, say what you feel, not what you saw in a movie, or what some guy on an online forum told you to say

.
If it went well, great, if not (she says something like "give me some time" or another form of "maybe", which = NO), then remain friends and go for other girls. Every guy likes more than one girl at a time, there is no way that a guy can like only one girl.
Hope that helps, it's roughly what I told Andrew to do, and it worked for him (at least up to the phone numbers and date part, although he got rejected on the whole 'girlfriend' thing because he's kind of ugly).
P.S. Girls are entirely different beings when they are around friends... they won't smile or say hi to you unless you say hi first, unless you are good friends; they won't seem as warm and treat you like just a 'guy' and not Jay, or whoever you are really. They laugh a lot more, and it is awkward to talk honestly with one because there are five others that stare at you and listen eagerly, ready to explode into laughter as soon as you say something. For gods' sakes, become friends with the whole group of girls she hangs out with, or get her alone. Usually walking with her and her group, greeting her, then tugging her gently and asking 'hey can I talk to you over there?' will get her to follow you and her friends probably won't, although they will stand where they were and stare at you guys, pointing and whispering to each other behind their hands, visible out of the corner of your eye, which still makes it uncomfortable because you are trying to talk to your girl while at the same time wondering what kind of things they are saying about you. So... if you get a moment alone, DO NOT WASTE IT. ^_^
P.P.S. Having a girl will pretty much take the rest of your time away, as it will be devoted to her. This may or may not be as enjoyable as a normal social life. If she's awesome, or is having sex with you, then it's probably going to be better. But as for me, some girlfriends were a drag; I'd had more fun with my homeboys in cross-country and our friends in hip-hop club more. Then again other girls are awesome and you don't mind being away from your sports team and friends. If at any point it gets boring, call it quits and justify yourself with the fact that teenage relationships are not meant to be permanent, and that you are not in fact oath-bound to stay committed, but can break away at any time.
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