how to do basic social interaction

I moved to a new school this year. I met this girl on like the second day, and acted weird as hell. I was really caught off-guard like I was about to cry cause I realized I wasn't going to make any friends(and I was right), and then the teacher does a partner activity and I'm like "kill me now". But then this random girl comes over and asks if I wanna work together and I said yes. But inside I was nervous as hell and was like HOLY SHIT SOMEONES TALKING TO ME AND ITS A GIRL AND SHES CUTE HELP. I tried to just say whatever came to mind cause I didn't want to get nervous and say nothing but what came to mind was kinda shit (I was also on bad side affects of antidepressants so I was like paranoid about everything going on). Also then I blamed her for making shit awkward :/. So then basically we never talked again and then like a couple months later I learn shes actually pretty cool not just cute. Funny thing is that I'm like 40% sure she liked me (who knows why, I used to dress like shit, had a haircut that said "I-I-I like p-p-p-pUZZLES" and certainly didn't show good personality) mainly because she went up to me, actually asked me a couple questions, got pretty shy halfway through conversation, and then a couple times after she like did the "look at them the glance away" thing. She definitely doesn't like me now (at least actively), and even seems to be getting pretty close with this other dude but I kinda just want to be fucking friends, I don't have any and that sucks kind of working on it, but not to any success. I've actually changed a ridiculous amount since then, like I'm not a shitty person anymore I decided "Hey If I'm not gonna have any friends might as well make it their loss", and I'm actually for once feeling good. But anyways, I want to talk to her, but I'm ridiculously shy and no advice ever helps but hopefully I can pull it off this time, I don't know how. Thing is that I only have one class with her, and her and people who sit around her all get to class before me so I have like no chance to go sit by her, and teacher teaches most of the class. I also tried to contact her on facebook like two weeks ago since I am probably never going to in person, but apparently she never checks that shit. But I was thinking of like going up to her in the morning and saying something, I don't know what the hell though. Something like haven't talked in a while, we should talk sometime or something and also CHECK YOUR GOD-DAMN FACEBOOK. Basically, what should I say cause I honestly don't know how to interact socially. Also, how do I get her attention and convince me that I can say shit while other people are around cause thats one thing that always makes me nervous.