Starting with a book would be great as you need to know basics of programming and the language itself. In the beginning just copy pieces of code and try to understand them. Functions and algorithms you know are like tools that you gather. I recommend that you always set yourself a difficult goal and then try to get as close to it as possible. Tutorials will help you with this. Just focus on what you find interesting or what could make your program more awesome. I think this is far more important than anything - play and experiment. It doesn't matter that you don't proceed in any specific order, you'll sometimes read a tutorial even after 2 or 4 years.
When you need to know more about a class, type its name and "livedocs" into google. The Adobe reference is brilliant:
http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/index.html
Getting inspired by random examples helps too:
http://hub.tutsplus.com/browse?utf8=%E2%9C%93&id=development§ions%5B%5D=Tutorials&tags%5B%5D=ActionScript
MSGhero
Every other thread in the flash forum.
milchreis.newgrounds.com has a good list of some basic stuff, but stuff like this gets asked a lot in the forum, so you might find some other good links.