Flash presentation of examples. Zip file (720KB) of the source files for the examples.
ActionScript summary and examples document
The Help information in the application is not bad. However, you need to be connected to the internet to get the full presentation (some of it is dynamically updated). The introductory tutorials are well worth trying out. There is also a fairly complete user manual, and a complete ActionScript object library. Note, however, that the ActionScript examples may be inconsistent, reflecting the evolution of the language.
While it is possible to learn Flash from the help sequences, I found Flash for Dummies very helpful, as it sets more context, and is also very good about pointing out common mistakes and problems. I've lent Marilyn my copy, and I'm sure she would be happy to share.
If you decide to do any significant amount of ActionScript programming (beyond basic support for dynamic UI elements like buttons, sliders and components), I strongly recommend ActionScript for FlashMX, the definitive guide, published by O'Reilly press. Not only does it explain the language in real programming terms, it also makes clear which feature are current, and which are supported only for backwards compatibilty. I could lend my copy briefly, but need it myself for the Flash work I am doing.
NB: The most recent version of Flash is Flash 8. It it is basically a superset of FlashMX, so the above references should still be useable.
Flash and databases (tutorial)
Flash support center