Well about 2 days ago my friend chad, was talking to one of his friends thats a girl called shay. I was sitting one the other side of the cafeteria and chad pointed me out and lied to shay and said I was his cousin. Well the girl that I happen to have a crush on christina(I dont really know her) was right next to chad and shay. Chad claimed that christina said I was cute after hearing chad's lie that I was his cousin. He said that christina didnt say it with great passion but in a more relaxed way. So how should I approach her? and what type of things should i say?

I would just pretend i did not know that chad guy said you were his cousin. one day smile at her, then just get close and ask her how she's doing, what she's up to.. if she's interested she'd talk back, if she says something like 'going to class' just say 'sounds like fun. ill walk you' and just keep on talking. make one or two negs and i wouldn't open kino until second time you have a conversation.

hey, im not even close of being a PUA, so if you want to ignore or somebody else posts something completely different, listen to him, im just trying to help

I disagree a little, I wouldnt open with small talk. It would get awkward real quick. Search the forum for Openers and see which one might apply to her.

You don't need any pick up arts to ask girls out in highschool.
In highschool it was very simple (at least for my highschool)
Just build some rapport (doesn't have to be much, just like 5 or 10 minutes in a conversation one day) and then the next day be like,
"hey will you go out with me? "
And then you guys are suddently boyfriend/girlfriend, ahh the good days
I think you will be okay. Because really, you don't even need any rapport, she is already attracted to you, just the main thing is don't be afraid.
To build rapport, ya
Start with a smile,
then the next day, just start talking to her about anything. Read for opinion openers, and neg her a lot. Negging is where you give back handed compliment. What you want to do is basically pick apart their personality, or things about them and make fun about it, IN A JOKING WAY. Make sure she knows you're joking, otherwise she will think you're a jerk. Depending on how hot she is, don't neg her too often, if she is a 6 use it very sparingly. if she is a 7, I find it is okay to use it every now than then... If she is a 9 or a 10, go crazy.