Need help talking to a girl?

I'm 17 in my senior year of high school. I have no experience with the opposite sex at all, I don't even have any friends that are girls. However, there is a girl I like and I want to get to know her, her number, ask her out, etc, but I just have no idea how to go about doing it. I'm quite honestly terrified of talking to anyone I feel attracted to. I have asperger syndrome so social situations make me feel very uncomfortable. I can be pretty sloppy when i talk and I tend to come off as a bit blunt/cold. I feel very self conscience about this so that makes it even worse and I start to studder a lot. I know that I'm fairly attractive, athletic, physically fit, and I value my intelligence most. In fact i'm very confident in just about every thing else in life except for when it comes to girls. I don't even know if im in the right position to be perusing a girl right now. I live with my single mother and were not exactly well off, so I only have a few pairs of cloths (which is embarrassing) and no phones what so ever. I've really only got one friend and I get very uneasy going out to public places (not that im to scared to, I just prefer not to). So I've basicly been staring at this girl all year with out a clue in the world of how to approach her. I'm extremely analytical so I've already figured out a lot about her, I just cant seem to find a way to talk to her or even know what to talk to her about. And because I have no experience in the dating scene that makes feel very inept, I need some advice on this situation.