If the girl you are interested in is shy it can be a lot hard to flirt with her. You have to take it slow when you flirt with her or you will make her nervous and standoffish. It can be hard to know where to begin when you first approach her but if you follow these steps you will learn how to flirt with a shy girl.
Smile and say, "Hi," to her everyday so she begins to feel comfortable with you. It's not a good idea to approach her and let her know you are interested right away, stick with subtle flirting at first.
Notice something nice that she is wearing and compliment her on it. Try to compliment her once a day so she catches on to the fact that you are interested in her.
Take it slow. When you notice that she is beginning to feel comfortable you should try complimenting her on a physical feature. You don't want to do this right away or you could scare her.
Ask her questions about herself and her interests. Shy girls find it easier to talk about things they are interested in so you should act interested and pay attention.
Find a common interest. If you find something in common let her know that you are interested in it too. She will feel more comfortable if she knows you share the same interests as her.
Let her do the talking. If you talk to much you may make her feel overwhelmed but if you come across as a good listener that is genuinely interested in what she has to say she will feel more comfortable hanging out and flirting with you.
Ask her out on a date. Choose an activity you can do to together instead of a more intimate date. It will take the pressure off of her and you will both have fun if you choose something active like playing pool.