How to approach a girl you've never physically met/held a conversation with and get her number?

Okay basic question. I'm in college, a sophomore and there's this girl in one of my classes I thought was attractive, throughout high school and freshman year of college I was always awkward around girls and I don't really know why. People who see me think I'm a normal guy I'm not bad looking at all I just get shy and awkward. Basically i was wondering if I told whoever answers this my possible approach if it sounds right or not.. thanks. My approach would be to sit next to her in class and strike up a conversation, start by introducing myself ask her her major grade etc. Then compliment her on somethint (not physical attributes) was told that was creepy something along the lines of I like her shirt or shoes whatever then hopefully by the end of class if I'm comfortable enough and it seems like she was interested ask for her number and say something along the lines of "hey do you think I can get your number so I can take you out sometime?" That is all. Thanks in advance for responses.