Should I add her on Facebook and what to do after if it succeeds?

So, I'm a shy guy and I have a big crush on that girl that was in my class last semester, I never had the balls to go to her and start a conversation... But, eye contact was made a couple of time ( she was not smiling though, i think she's shy too because we made eye contact more than one time) and i don't know if i should add her on FB, we have like 60+ mutual friends. I'm just really curious about her and i think there is a chance she might like me. So, should I add her and if she accept, what do I say to her and when? I have never been in that situation before. ( sorry if there are errors in my text, English is my 2nd language)
Should I add her on Facebook and what to do after if it succeeds?
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