Smile. Nothing is friendlier and more welcoming than a smile. When you make eye contact with her, smile because it's very hard not to smile back at someone who's smiling at you. This will also be a clue to her that you like something about her or that you're interested in her. Every time she looks at you, just give her a big smile. But don't stare and smile for too long or it might start to seem odd. Simply smile, let her smile back and look away.
Make her laugh. Girls are attracted to boys who have the ability to entertain. People always want to be around a funny person. Being funny also a great way to break the ice; start with a clean joke. Don't tell dirty jokes because she may not appreciate that type of humour. Before you tell it, ask her permission, "Can I tell you a joke?" She will most likely want to hear it.
Be nice and sincere. This may seem obvious, but girls appreciate when a boy treats her nicely by doing considerate things like carrying her books or buying her lunch. Some boys will be nice when they're alone with a girl, only to act tough and aloof when his friends are around. It's a sign of confidence to not care about what his friends think but to care more about being nice to her. Another way of showing sincerity is by restraining from bragging. This can be a sign of insecurity which will counteract your desire to appear confident.
Compliment her because girls love compliments. You don't have to overdo it, but keep it simple. Say something such as "Your hair looks nice today," or "I like your shirt." Choose something about her that you like and let her know. This is a very powerful flirting technique. Complimenting people automatically disarms them and makes them open up and easy to approach.