Compliments are the classic flirting method, but some things become classics for a reason. Compliments, in addition to giving her a little boost, show that you're observant and that you care about other people. Focus on a genuinely strong point about her that really strikes you. You don't have to stick to the physical: you can also compliment her singing voice, the way she interacts with her friends or just about anything else that catches your interest. Don't go too far and don't belabor the point: just let the compliment stand and let the conversation flow from there.
If she has clear, well-defined interests, spend some time looking into them. Although you shouldn't pretend to be an expert at something you're not, being able to talk with her about her favorite band or subject shows not only gives you a conversational in, but, much like compliments, shows that you're observant of her individual traits and are willing to extend yourself in interpersonal relationships.
Another way to show that you're really interested in a girl is to ask her questions about herself. This shows that you care about more than the way she looks, and truly want to find out more about the person she really is. This also helps you avoid talking too much because of nerves. Really listen to what she says and use this to help carry the conversation forward; for more on active listening, see Resources below.
Confidence is an attractive feature in potential mates. According to Jeanne Segal, PhD, et al., other people can tell when you're tense or nervous, and this can put them on edge, too. Although approaching a young lady to hit on her might make you a little sweaty and turn up the dial on your nerves, projecting an air of confidence--even if you don't feel it--will make things go more smoothly. You might even prepare what you're going to say first if it helps you assume a more relaxed air.
The best way to find a girl you're interested in and who will also be interested in you is to be yourself. While it's perfectly acceptable (and advisable) to put your best foot forward, changing too much of yourself to accommodate the object of your affection means that you're not being honest with her--or with yourself. Be open about what you're looking for and what you're interested in, and you'll find yourself flirting and dating much more effectively.