How to Get the New Girl to Like You

1.1
Introduce yourself to her. Since she's new, she probably doesn't know very many people. Just the simple act of introducing yourself can really make an impact on her.
Approach her confidently, greet her, and tell her your name.
Ask her how she is coming along in your school and if she needs any help adjusting.
2.2
Make casual conversations whenever you see her. She may already have friends she talks to, but that doesn't mean she couldn't use one more. If you sit by her in a class, pass her in the halls, or wherever else you may see her and and have the opportunity to talk with her, do so. Make jokes (in good taste), ask questions, and tell interesting stories. Just get a conversation going and see where it leads.
3.3
Make sure she has the right friends to talk to otherwise they will tell you all the weird or embarrassing things you did earlier.
4.4
Give her your phone number or ask for hers. Be casual about it. Tell her to text you sometime. If she gives you hers, text her later in the evening (not as soon as you get home) to give her your number. Every once in a while, text her to ask what's up and get a conversation going.
5.5
Ask her out somewhere. You can either do this in person or on the phone, whichever you think would be easier for you. Invite along a couple mutual friends, or several of yours and ask her to invite several of hers, to make it less awkward. Make sure she knows if it is a date or not.
6.6
Continue to hang out with her. Slowly, your friendship will continue to build. It could end up as a romantic relationship, or just really good friends.