Does she like me and how should I approach her?

I have this girl in an art appreciation class and I sit slightly behind her to her left. Occasionally, she will look back in my area where i sit. I have made eye contact with her occasionally. I have seen her flip her hair, though idk if tht is a convincing sign, and today when the class was finished she went out the back door and I went out the front, she passed me again and while i was holding the door for a few girls she glanced at me real quick and gave a subtle smile to herself. I think next time I need to smile at her when I make eye contact. How should I approach her after class? Today I failed because after i held that door she was walking right in front of me and i didnt do anything lol.