How do I start this flirting?

There's a girl I go to school with. I know who she is and she knows who I am, but that's really it. We know each other in passing, nothing more. But she's really cute and I would love to have a relationship with her. I've never had a girlfriend and I suck at flirting. Whenever I like a girl, I end up getting too close to her before I really start to hint that I like her. By then, I'm friendzoned.

How do I start this without ruining my chances? FWIW, she's a quiet and reserved person. From what I see on her Twitter account (don't judge me, we all do it), she's a hopeless romantic like me. She's not the type of girl that guys are always going up to her and hitting on her. So basically, going up to her and making sexual flirty comments will turn her off. That stuff may work with some girls, but not with her.
How do I start this flirting?
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