Seeking guidance in attempting to pursue a relationship.

To begin with, I'm new around these parts, so greetings, denizens and veterans of this board alike.

And to make a painstakingly long story mercifully short, relationships have never been an area in which I excel. In the 18 years I have resided upon the face of the Earth I have only been within a single relationship which, needless to say, ended in hormone-addled monsoons of tears.

Having began university life back in September, I've felt that epiphany I have so long and impatiently awaited approaching. A new perspective on life, so to speak. One of my primary motivations behind going to university was to break out of my antisocial comfort zone for good- actually make something resembling an effort to befriend others and become an average, morally upstanding member of society, hell, maybe even defrost my icy heart.

But I digress. Anyway, since arriving, as fate would have it I was assigned the exact same timetable as one particular girl, who will for the purposes of this confession be referred to only as "Jane Doe".

To contextualise, I am one of the most insecure and socially awkward people you'll ever meet, given how I obsess over every single one of my inadequacies- everything ranging from my weight (I weigh 11 stone) my height (I'm 6'0") my appearance, dress sense, etc. And I constantly worry ponderously what people may be saying behind my back (let's just say I have severe trust issues as a result of past experiences) Everything about me is thoroughly unremarkable.

In the other corner, we have "Jane Doe" who socialises seamlessly, is considerably attractive, strong-willed, etc. i.e. everything that I am not. She has, very recently, jumped ship from her sinking relationship, meaning I have been given a chance that is mine to take.... until someone else inevitably beats me to the punch. Even so, of all the myriad boys she could have, in what distorted, tyrannical negative universe would she choose Captain Cardboard?

Okay, so I've turned this into an extended navel-gazing session and maybe, just maybe, people are right and I do put myself down far too often. My purpose in writing this post is to seek rational, edifying advice from someone less impartial than myself. The two of us have a solid friendship right now, but as of yet we haven't socialised outside of class, primarily because of me being two yellow to ask, but that's beside the point. I know, for definite, that I am developing feelings for her, as saccharine as it may sound, and I will never know unless I try. So I ask the burning question:

What do I do now?