I met someone at a dance and I want to know them. what do I do?

I met this girl at a dance at my school. she already had a date, and she was from another school. as it turns out, I think she liked me better than her date (quite obvious, actually). anyways, I am sort of a quiet, shy intellectual of a person. I went there because my school works on a participation-point based system, with a minimum of three to come back next year. I seldom go to dances to dance. I did not know to dance until I met her. I usually sit and wait for the dance to be over. but then, I met her. we danced. I had the most amazing feeling, like something I have never felt before. as an intellectual, I tend to distance myself from the others, so it is hard to find love, let alone keep it. in the end, we had a good time together. but, in the end, like all things, the dance ended. I did not know her name, and I did not know if we were to see each other again. she had found some ways to subtly hint that she was into me (not so subtle after all). and, as it turns out, I feel the same way and I want to know her, but what am I to do? I do not know where she goes to school, I do not know her name, and I do not have her number. I do not know if I will see her again, so how do I find her? where do I start? should I ask her date? should I ask a mutual friend? as you can see, I am not one for relationships, as I do not know where to begin, but I want to. by the way, I am fifteen, if this helps, and I go to a military academy.