Hello, emsee, glad you're hear and glad you're giving AA a shot. My experience with the handed out numbers is you just call them. At least in this area, those telephone numbers are for you to be able to reach out and hear a friendly, understanding voice when you need one. I did make some calls, and it felt a little funny calling what was essentially a complete stranger, but think of those numbers more as hotline numbers to help you when you're struggling and need to talk. That's how I treated them.
My actual sponsor that I have I got by going to meetings and listening to what people had to say, hearing a little bit of their story and experiences and attitude. Finally, I just asked someone if they had a minute after a meeting and asked him if he was interested in sponsoring someone. Bill is 34 years sober, was about the same age I am now when he got sober, and has a similar outlook on life. It's been a good fit, at least thus far. Good luck and keep coming back!