How to flirt with this different girl?

So I recently met this girl that I've developed a crush on. We met 4 days ago to be exact. We are in college together, and we are currently taking classes over winter break. There aren't many students on campus, so there's a small group of us that hang out almost every day. We have really seemed to hit it off. We have a very similar sense of humor, so we make each other laugh a lot.

The thing with this girl is that she is not like other girls. And I don't mean this in the cliche way that "she is just so much better than other girls." I mean, she has a sense of humor you wouldn't expect a girl to have. She doesn't like drama or really cheesy interactions between guys and girls. So, I'm not exactly sure how I should be flirting with her. She's general pretty quiet and shy around people she doesn't know well. But she is very outgoing with her friends (and when she's drunk, but we all are haha!). She's never had a boyfriend, and I've never had a girlfriend. What would she like?

I talked to my friend about her (the one who introduced us to each other) because he knows her much better than I do. He says he doesn't see why I wouldn't have a shot with her and that she is "different." I know what he means; it's what I was saying before. She doesn't act like most girls, and I don't think she would like some of the ways guys typically flirt with guys.

She is still kind of shy around me. She is becoming more outgoing, but she doesn't really seem to direct things at me. When she does, she seems a bit more shy. I'm not sure if she likes me or is just still getting comfortable around me, but that's not what I'm worried about here. I just want to know how I should flirt with her without her getting annoyed with me.
How to flirt with this different girl?
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