I had so many missed opportunities in my life. There were times that girls had crushes on me and I'd say or do something that made them hate me. Other times, I chased after girls I liked and it was just a way to waste my time and make me feel awkward when I was around them. In my high school years, my heart would start racing when I was around or was anticipating being around girls I liked. Not fun, since the presence of someone I liked made me feel like I had just ran a mile.
Eventually I found a girl I loved, and I still love her. My advice for you is pretty cliche, but it's definitely true. Get out there. Join a school club or an out of school volunteer group. Be social and hope to Jebus a girl falls for you. Some people would tell you to ask a girl out, but if you're shy, your proposal wouldn't be very effective anyways.
Other methods:
1. Just be nice. Talk to her. Remember her birthdays, bring her candy (even if you're not friends).
2. Befriend her friends. If you know her friends, it's much easier to befriend the girl you like (and then it goes on from there).
3. Break the barrier between school/club and hanging out. Ask her to do something with you (movie/social activity works best). Even if she says no, she'll appreciate that you asked.