I had this exact problem several years ago. I was a very shy person, especially when I was younger, and I'd never like/want to step out of my 'comfort-zone'. If I knew I needed or wanted to, I would get very nervous. One day, I met a girl. I'd seen her a couple of times before, but very briefly. To start off with, I was bricking it, literally. To be honest, I bet she thought I was a right nut-case. After a few minutes or 'random' conversation, the ice broke. I started to feel more confident then ever. We started chatting about more "normal" things, you know, stuff kids our age should talk about. We then started laughing and passing the odd joke. Next thing I knew, we were sat next to each other at he Cinema.
My advice for you, Necromancer, is to gradually get to know. It could take a while, it might not. This, from my experiences, will help boost your confidence when you're about to chat to her. I mean, if you know more about her, you'd know what she likes/dislikes and then you'd be able to talk on a more 'parallel' level. I suggest taking things one step at a time, and also, if your friend is a supportive one; I'd talk to him. Tell him how you feel about his sister, ask if he thinks she feels the same way.
I hope I helped, Bud.