Although I consider myself sort of "a natural" once I've established a base-level of comfort with a girl, I have the most trouble getting to that place. Once I know the girl and she knows a litte about me, it's smooth sailing. How do I get to that point with a stranger though?

For example, today I arrived at one of my classes late and instead of sitting in my normal seat found a new one next to the cute girl in class. The teacher was talking so it wasn't a great time to start a conversation, but I made small / insignificant talk about the assignment due tomorrow. How do I transition this to something more substantial? Especially without coming off as if I'm interested?

I was thinking I'd ask for her name but I hadn't made any small talk with her friend who always sits next to her and I thought it'd look weird if I asked for her name, specifically, and not ask the names of the others sitting around me.

Even if I had asked her for her name, how do I turn this into a number? Into a date?