How should I ask her out?

I work in a very small library on a university campus. Every Tuesday and/or Thursday, a girl comes in, and does her homework or just messes around on her computer. For whatever reason, I feel some kind of attraction/pull towards her and would like to get to know her outside of the library. Most of the time, there are only a few other people in the library, including the cute girl and myself.

What would be a good way to ask her out, without being weird, and without drawing attention? I thought it would be best to ask her out for coffee.

Please, let me know what you would do. Thanks!