How should i ask this girl out?

Best thing to do is to start a conversation with her. She comes there daily, but have you ever said hello there nice to see you again? Just say hello. And during your break, if she is there, you can go ahead and approach her. Seems scary you might be thinking, but think of it as approaching and talking to a college friend. Greeting and smiling at someone, builds rapport, even if there is no conversation yet. Ask her facebook account, add her. If the coffee shop seems so full all the time and there is no way in the world you can get hold of her, getting her FB account is a better option. Then you can start knowing more about her background, etc and her interests. Find something you two have in common and use it to your advantage. ;) Then you can invite her out without sounding like you are a total stranger to her.