Hmmmm, this sounds like a romantic interest. Even so, some of the rules for friendship apply: you need to be friends before you go romancing, right?
First off, people tend to behave differently in public than they do in private, especially in school. If you really want to get to know the girl, try to find some privacy to introduce yourself.
Try to engage her in conversation. People in general start to open up a little when they can talk about their interests. If you can get her to talk about ANYTHING you are on the road. This applies to people in general: they like to be drawn out, especially regarding the things they have interest in. The temptation is to make yourself look good by "showing off". Avoid this, and concentrate on learning how your potential friend thinks and feels. Remember you can always talk about the weather. That's a starting place, and most people recognize that it is a social sort of introduction that says "I want to talk to you and get to know you". Another fine introduction is to compliment someones work, it's always an ice breaker.
Friends in general are people with whom you have things in common with. Just by joining the forums you have put yourself in a good place to make friends, since there are many things we all hold in common here. Personally, I regard you as a friend. We have had contact, and I have found you to be polite. This is the way most folk feel: to regard all as friends at least in potential until they prove otherwise.
Being polite, remembering your please's and thank you's, having sympathy, keeping confidences are all important to making and keeping friends. Also, remember the door swings both ways: it is not always right to have a friend call on you, visit, provide gifts, ring you up without responding in kind, and without being asked....and often over the objections of your friend. Friendships are active things, and must be persued by both parties.
As to possible rejection: this is always a possibility. Asking for a "date" even if it is just to see a movie or visit together is always a nervous thing. Remember to go slow, and not push. If there is interest, it will show eventually. If not, be realistic and move on. Sooner or later you will find someone who can relate to your personality, even if you are unsure of its quality. If you are rejected, it does not mean you are "no good", only that this situation or time was not right. There are other possibilities, and the quicker you can move on to them, the richer your life will be. CArrying the torch, and waiting for a miracle is often a waste of time. If Sue says no, go ask Rosie. Sooner than later you will find someone as lonley as you are. That's just the way the ride goes, but if you refuse to try, you will never fly! You only have so much time in life, so don't waste it moping around in regret.
Keep in mind that beauty is just skin deep, and love and friendship have little to do with the outside package. No matter how "pretty" a person is outside, after 5 years or so in a romantic relationship it won't matter all that much. What *will* matter are the qualities of generosity, sympathy and respect. If they are missing, then the relationship will go by the by. Everyone wants the pretty ones because we are told that is the thing to want. Guys are after the pin up girl, and the girls all want that suntanned lifeguard. They eat their hearts out if they can't land their dream, while in the meantime someone worthy of that love and capable of returning it is standing right next to them, every bit as longing as they are. Keep your eyes and heart open to these possibilities.
Giving is always a good way to make friends, but you have to be able to draw the line between making friends and buying friends. There is a difference.
Friends forgive, and do not hold grudges even when they disagree, they can just agree to disagree and get on with it. This is part of the mutual respect that friendship demands.
Friends do not gossip about, or put down friends, but stand by them. I was a grade school reject, but I managed to make a few friends anyways: those that did not care what everyone else thought and said about me, and were willing to befriend me despite the heat they got for it. THESE are the friends I would have, not a bunch of social fakes trying to be cool, but rather those willing to think for themselves! Remember that in your age bracket, there is much to learn about being social, and what might appear hopeless now may later change. Life holds many surprises: I now have more friends than I could ever have imagined during my pre-teen years when I felt I was worthless. In time, you will find that many of your other classmates have had the same thoughts, feelings, and uncertanties. It is a common part of growing up, and it will pass. Most of this sort of imagining is pure paranoia that the whole school thing seems to produce - it's really mostly just in your mind.
Try to be a good man the best you can, and the rest will follow. IF there are those that can't accept you for the way you are, and you are trying to be the best person you can, then their opinion is absolutely worthless, and their "friendship" would be as well.
I admire your asking this question. It shows a person of concern and sensitivity: both great qualities for making and holding friends.