Coming from a girl, I would say try your best to find a conversation starter. Something that interests you both. If you don't see any evidence of her being a video game fan, you could start by asking, "I've never dyed my hair pink, is it hard to get your hair like that?"
Just go up and ask casually. After that you could ask questions about work or hobbies, anything that isn't too personal. If you see her in a restaurant or cafe or whatever, you could ask if she goes there often. Find out where she likes to eat or drink. If it doesn't look like she's trying to get away from you or not really answering your questions, at some point ask, "oh I like that place too, you want to go there together sometime?" If she is uninterested, leave her be, please. =)
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