Approach her indirectly. This will allow you to engage her in a conversation without making it too obvious you are interested. There are so many opportunities to strike up a conversation if you just pay attention. If you notice she has a watch, you can ask her for the time. If you are at a mall, you can ask her where a certain store is. Then seize your chance to strike up a conversation with her. Since she is not expecting to get hit on, you will probably be able to talk more casually and she will too.
Compliment her, and really mean it. Her hair, outfit and shoes are perfect choices, because she will have put a lot of effort into deciding these things. She will appreciate when a person notices her efforts to look nice, especially a person she is interested in.

Try telling her that her beautiful skin makes her glow or that you love the shade of her hair.
Tell her that her outfit looks great, or that you love how she paired her shoes with her outfit.
Try to avoid doing anything like suggesting that she is the best-looking woman in her group of friends. She may take this as an insult to her friends, rather than a compliment to herself.
Be nice to her friends. If she is with a friend and you exclude the friend while chatting her up, she will feel guilty. She may leave you to go hang out with her friend, so be polite to her friends too and include them in the conversation.
For example, if you ask the girl you like if she would like a drink, turn to her friend after asking her and ask "Would you like anything too?” You will not only seem generous, but also considerate.

Tease her. This didn't stop working just because grade school is over. A little light-hearted teasing can liven up the conversation and add some humor. If she likes the wrong sports team, or listens to an artist you don't like, tease her about it a little. The key is knowing when to quit. If she isn't laughing and smiling along with you, it's better to stop.
For example, if you notice she has a Patriots keychain, you can let her know you have an air pump at home and can swing by and inflate some footballs if she wants to trade numbers.
Tell her you're busy. During your conversation, let her know you'd love to take her out but you're just so busy lately. This will make you seem in demand, unavailable, and thus more desirable. Instead of playing hard to get, she will then have to work to be worthy of your time.

Give her some space. You struck up a conversation and it's going well, and now you need to know when to quit. Excuse yourself to use the restroom, or go visit another friend or acquaintance if any are around. Just be sure to let her know you'll be back so she doesn't feel abandoned. Show her the whole night doesn't hinge on whether you talk with her or not. This will also give her enough time to arrange for her friends to find something or someone else to do.
Giving her some space may also make her miss you more so she's more eager to talk to you.
Take a wingperson. When you head out to get girls, a friend can help keep your target's friends busy. You may need back up if the girl you are trying to get is being advised by her friends to move along.
Choose your crew carefully. Take a close look at your friends. They don't need to be Ryan Gosling to hang with you, but they should be pleasant to be around.