How do you get a girl to go out with you?

Try getting together somewhere where you can talk and get to know each other. Dont Rush it, try to get to know the girl better before you ask her out. Give some nice paragraphs and cute sayings to win her over. Dont be afraid of her.

How do you get a stubborn girl to go out with you?

Listen actively when she talks about her interests, and be enthusiastic when talking about yours. Ask her for recommendations for new things to try, watch, read and listen to. Go where you know she might be. Dont be creepy about it, but listen for cues about things she likes and look into them for yourself.