Adobe After Effects is the software program for creating special effects. It was used just recently to produce the Oscar winning visual effects for Hugo. Video Copilot is the place to go for tutorials for After Effects. It has both beginner and advanced tutorials.
The basic training tutorials are in this link.
Here are the individual links to the ten basic training tutorials:
1. Introduction All the basics on how to navigate the program
2. Effects How to add simple special effects using the effects and presents pallette to find specific plugins.
3. Animation Animating and adding keyframes. Adding motion blur to animated layers and short cuts.
4. Keying and Transparency How transparency works in After Effects from simple colour keying to transfer modes.
5. Motion Tracking This tutorial covers several kinds of motion tracking including stabilizing a shaky shot, performing a sign replacement and motion tracking video to incorporate motion graphics seamlessly. This is an advanced tutorial.
6. Time Remapping How to create slow motion and how to speed up frames.
7. 3D Integrating Basics of 3D with depth of field covered and particle system. Advanced tutorial.
8a. Titles Part 1 8b. Titles Part 2 Fun with text.
9. Expressions: Scripting Language in After Effects. More advanced tutorial.
10. Rendering: Exporting the finished movie How to export out your files to various formats and compression rates.