Okay, I've looked around my school, and I got an idea on how other kids succesfully ask out a girl.
First thinkgs first, try to give her attention before talking to her. Don't start an entire conversation with her, but offer to help if she needs it, display friendliness without seeming to eager to be around her.
This part sounds weird, but make it clear to her that you're not an NPC and an actual person. Just have conversations around her with your friends, again without making it obvious that you are meaning to be close to her. Remember to keep the conversation friendly, but put your personality into it.
this should work as long as you don't be too obvious or outgoing.
I've already stated this, but make sure you keep conversations around her friendly, but put personality into it.
