Does this girl like me? What should I say to her when I introduce myself?

[Bob Bobby]

I noticed a girl checking me out at lunch at my college the other day. I noticed this out of the corner of my eye. She kept looking at me for a few seconds every few minutes. At one point, I noticed her smiling at me and her friends looking at me as well. I'm a shy guy to begin with so I looked at her while she was staring at me, then I looked away and continued to listen to my friends converse. When she wasn't looking I looked back at her and I couldn't help but notice how pretty she was. And just the other day, I noticed her as I was walking up to get a drink at dinner. I saw her glance at me for a few seconds, then turn away pretending to not have seen me. Once I took a seat at my table, I noticed her get up to get a drink and as she approached her table, she was looking at me again.

So does it sound like this girl likes me or not?

I like her and would like to get to know her more. I found out her name, but I have not met her in person yet.
What should I say to her? I don't want to come off as boring or obnoxious by asking too many questions.
Is it okay to tell her that her eyes are pretty?

I've already done some online searches, so I don't need any info on stuff like "being myself" or "being funny," although any tips relating to those would be helpful

Thanks!
Forgot to mention that I friended two of her friends on fb, then I was able to find her and added her. She has not communicated with me and I do not want to say anything to her on there until I meet her...

 

[Honest guy]

well girls don't stare unless they like you so yeah. Well you could go about it in a funny away like when she is looking at you go to her and ask her if their is something wrong with your face and why do you keep staring at me.Throw her off a little bit and smile and introduce yourself in a funny joking matter then tell her that's she is pretty and if she wanted to hang out some time.