Best way to get involved with a girl from my class?

Hey r/askwomenadvice! I'm currently a junior in college studying biochemistry, and there's a really attractive girl in my physics class (it's for the MCAT's) who studies neuroscience. We're into similar rough-tough-contact sports (she likes/plays hockey and I'm a starter on our rugby team), and she goes to the gym in the early mornings and if I go for a morning lift I always see her there. In my physics workshop she laughs at the things I say and sits facing me whenever we get into groups, and I've caught her looking at me a few times too, so I think she's interested in me. The problem is, I'm so fucking awkward with people sometimes. I've never had a legitimate conversation with her, and I was wondering what the best way to start to get to know her is. I have no expectations from it, other than I think we'd get along and she'd be a cool friend to have (and possibly more after I feel it out). I just don't want to do it in a weird manner and fuck it up as I am prone to do.

TL;DR - How do I start to get closer with a QT3.14 in my physics class?

Thank you guys!