I'm no good at picking up women, despite the fact that I've never really tried hard. I think friendship is a great place to start, and if she seems to be interested, something else may blossom.
but if you want to meet women, go to where they are, and start talkin. The great thing about talking to strangers is you don't really have to worry about seeing them every day and being awkward. Also, strangers haven't heard any of your stories or opinions a hundred times already, so you seem that much more interesting
It's ok to be nervous, don't try to be too outgoing if that's not who you are, but avoid the label of "blushing blustering bumbling baboon," shyness is only cute to a certain point. If you don't want to talk so much, ask the girl about herself. That way you get to know her better, and can have some time to build up your confidence to maybe talk about yourself if she asks.