First of all, here’s a very incomplete list of big things added since version 4.0, with links to the high-level Help pages on the Web:
– 3D layers
– text layers and text animators
– expressions, which are pieces of JavaScript that you can use to animate things and link properties together
– a scripting interface
– color management
– painting and cloning tools
– parenting and null layers, both of which features help to animate many things by connecting them to one
– animation presets, which allow for saving, reuse, and exchange of combinations of effects and animations
– improved render automation and network rendering
– Clip Notes review features
– lots of new output and input formats
– new customizable docking workspaces
– lots of integration with other Adobe applications
– motion tracking and stabilization
– Puppet tools
– Brainstorm
– shape layers, for creating and animating vector graphics within After Effects
– lots of new effects
I’m sure that I missed a lot, but—yowza!—that’s a big list.
I recommend reading After Effects Help on the Web, not the Help document installed on your computer or the printed User Guide. Even if the Help content itself isn’t what you need, the Help pages on the Web contain hundreds of links out to video tutorials, blog posts, forum threads, and other useful resources. Here’s a link: After Effects CS3 Help
If you’re not finding the information that you need in Help, you can leave a comment at the bottom of any Help page by clicking the Add Comment button and ask for additional information. The same applies if you find errors.
One good resource for free video tutorials is “Adobe Creative Suite 3 Video Workshop”. The Video Workshop leans a bit toward the newer features.
I also really like Aharon Rabinowitz’s video podcast and Andrew Kramer’s stuff at https://www.videocopilot.net/.
John Vondracek has a series of introductory video tutorials on motion graphics in After Effects.
If you prefer printed books, I recommend _After Effects Apprentice_ from Trish and Chris Meyer. (See the CyberMotion website.) The Meyers have a few more advanced books, too. These books are considered by many to be indispensable tools for learning After Effects. I have all of them on my desk. Also useful is the _After Effects CS3 Professional Classroom in a Book_, which walks you step by step through many features and workflows.
See the “After Effects resources” thread in the Adobe user-to-user forum for recommendations and discussions of many other resources.
Of course, as you’ve already determined, this forum is a good place to ask questions. If you can’t find some information, ask here. We’ll try to point you to what you need.