How do I ask out a shy girl I like?

try to talk to her more in school, and then eventually ask her if she wants to hang out, don't call it a date just yet, if she;s really shy she'll get scared - even if she really likes you

That's easy because she's a shy girl...just talk to her and in the middle of the conversation ask her out. She won't refuse she seems to like you so there will be no problem asking her. Good luck!!