Hi Andy,
I like all of the responses so far. I recently completed a First Responder course at my local Hospital and I also live in a rural area.
After taking the course, I think it's VERY important that based on the questions you are asking, you too should track down such a course and take it, even if you are not planning to help a local volunteer FD/Ambulance team. Many people take the course as part of work safety as well.
You realize quickly during that course that even armed with all the information you are digesting you have just scratched the surface of what there is to know.
Keeping yourself safe is job #1. If there's something you think you can help with and not injure or infect yourself doing or you feel you have a moral obligation, the answer is "maybe" help and that's putting it politely. You could easily injure yourself or others making it worse. Calling it in and staying on with the communications is probably one of the best things you can do without any training.
It's funny, when I first started following this site, I was interested in First Aid and had many of the same questions as you. I was chastised pretty nicely for not understanding the difference between a bandage and a dressing. Now I know the difference and I also know why I was chastised. The pros know this stuff and unless you go about learning it yourself, you probably ought to stay clear and help only peripherally, else you will get in the way or injure yourself or someone already hurting.
Given your questions and my own assumptions about how you feel, my guess is that a class is in your near future. Call your local Ambulance and they can put you in touch with the people you need.