How do I approach her?

Hi, started college few months ago and I saw this attractive girl that I wanted to approach but I never know how. I don't really see her often because she's from a different course. When I do see her, she's always wearing her earphones and studying or sitting with her group of friends which makes it hard for me to approach her. I don't really have problems approaching random people, saying hi and starting a conversation but I find it really hard to do that when I am attracted to that person. Today I walked past her and made eye contact with her but she looked away quickly.

Would it be a good idea to just walk up to her and say "hey! I seen you around sometimes, just thought I introduce myself."? A guy told me she's a nice person but nobody really approach her because they think she's out of their league or whatever and told me good luck if I want to approach her. I am guessing maybe because she's really tall and doesn't really smile. Maybe that's intimidating or something. She gives off that quiet type of girl vibe too...

I assume she notice my presence or the fact that I exist because we took the same train once or twice and she looked me a few times before. She don't really make eye contact with me when we past each other most of the time which kinda makes it hard for me to just smile at her and say hi!...any ideas how to approach her? Thank you!

Yeah, I think what you have in mind is fine. You can also try writing her a note with your cell phone number or other texting info. Or sit next to her on the train and talk to her. I remember on my last day of college I found one of my classmates sitting on some stairs and she blurted out moment I realize I could have had a chance. So definitely take a chance and make contact with her some way, any way.

She blurted out that no one had asked her out during the entire four years at college. And at that moment I realize I could have had a chance with her.

Thanks DanZee! Will try to work up the courage to do so.