There are several essential techniques shown, and the final effect is easy to replicate. As usual there are several additional ways to do this effect. You can adjust the method by using a square image size in powers of 2 (512 or 1024 for example), so that the image is seamless when the Clouds filter creates the fill. Layers can then be used as a seamless tile for animation with the Offset filter in AE. Though spare, you can get away with only 3 layers (as seen in at least one 3rd party fog filter). Other additions should include a light touch of a favored distortion filter and/or 3D moves. Sebastian Sulinski showed how to create a seamless animation loop in another tutorial, Animated clouds effect with Photoshop and After Effects. Here's ABC Episode #26 (mentioned above) from AdobeTV:
A less archaic approach that may require more experimentation is just using the Fractal Noise filter in After Effects; for background, check out the resources in the AEP post Spare time for Fractal Noise.
The use of Fractal Noise for fog is discussed (on page 3) by Mark Christiansen in Climate: Air, Water, Smoke, Clouds in After Effects 7.0, a free excerpt from the book After Effects Studio Techniques. An alternative is the Turbulent Noise filter, which is an updated version of Fractal Noise. It creates smoother animations, but doesn't doesn’t have Cycle controls to create seamless loops. To create a seamless loop of animation using Fractal Noise, see Christiansen or After Effects Help.
Dean Velez also showed how to use Fractal Noise in the Total Training course Advanced Adobe After Effects 7 Pro. Here's a video excerpt if you want to sit through a commercial:
See also a few related implementations in tutorials by Video Colpilot, for example Smoke Screen (using puffs of smoke as particles) and Stabilize Shaky Footage.