How can I win her heart?

Alright, I'd like to start off by saying that I'm not deluding myself that I can actually make a girl fall in love with me. I know that's not how it works, but I also know that I don't just want to give up.

You see, I met this girl in June. We dated for a while, then decided to just be friends; then things did eventually happen anyway and for a while we let that continue without defining it; and then eventually she told me she simply didn't feel she wanted anything more with me than what we had, so we decided to stay friends.
During this time we've developed an incredibly close friendship. It's not simply the case that we can talk to each other about literally anything that either of us might think or feel, but I have a connection with her that I have never experienced with anyone else, nor do I expect to experience such a connection with anyone else, ever, even if I were to eventually fall in love with someone else. And I know she feels the same about me.

Despite that though, it is the case that I'm madly in love with her and she isn't in love with me, and it's not that I'm not willing to accept that, but she means so much to me and my feelings for her are so strong that I don't want to give up without a fight. I want to give this everything I've got, which is why I'm asking this question.

Specifically, what I'm asking for is advice. What have you learned from your experiences with love and relationships? Have you ever gotten out of the 'friendzone' (I don't like that term because of its negative connotation, but it'll have to do) and if so what was is that made the other fall for you? Has a friend of yours ever won over your heart and if so what was it that made you fall for them?
How can I win her heart?
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