Start talking to her!

Soo, I like a girl in school and 3 years ago a she asked a guy in my class if he wanted to be her boyfriend and he answered yes. But a few weeks later they broke up, they never told me why. Now they had been together again and I have a strong feeling that their relationship is getting weaker and I just want to make a push and start a relationship with her but there is a problem... she is one of those girls that I never talk to or never get in contact with so I need some tips of how to start talking to her!

It's amazing sometimes how far a simple "hello" and a smile will get you. Just start small. Ask her what she thought of the class or how her days going then let the conversation flow from there.