1st girlfriend ever...?

Hey guys,
I recently started college and I sit next to this most amazing and stunning girl in one of my lessons. But I don't know her too well.
I Want to get to know her, but I don't want to get to the friend zone area and then want to ask her out.
If I want to ask her out, what stage of getting to know her would be best.
Also, what would I say as I am quite shy in girlfriend sort of things, etc.
BTW, I also want her to know me a little so if she does say yes then it would last.

I hope you guys get where I am coming from :-)
Any help is appreciated, thanks

Behave as if you know what you are doing. The trick is never doubt. Let her think after but you look ahead. If you say come with me you should mean it. Girls are stupid. They believe males. They follow the one who is the most dominant.