If you would like to learn to do more with After Effects, there are plenty of resources out there to help you. Adobe's site has a couple tutorials. Creative Cow also has a ton of really good tutorials and a forum. This is the best place to further your learning, in my opinion. There are also a ton of good books available which you can purchase. Last but not least, don't forget that there's an excellent manual/help file!

Because its hard to know exactly what you need to learn if you don't know what everything does, I'll try to explain the uses for most everything that wasn't covered in the tutorial here. It's your job to go out and learn to do these things, using the resources listed above.

Nesting Compositions
Nesting compositions refers to putting one composition inside of another composition. You may wonder why you would want to do this, but once you begin work in AE, it will quickly become apparent what a useful feature this is. Let's say you have 5 layers of images on top of your video. You want to apply a single effect to all of the image layers, but NOT to the video layer. All you have to do is pre-compose the 5 image layers into a composition, then apply the effect to this composition. When you are doing motion graphics, this is probably the single most important thing that you will need to know how to do!

Masking
Masking is what you wanna do if you want to isolate a character from its background, and put it somewhere else (like in the Tainted Donuts AMV). Creating and animating masks on the character is quite easy in AE. It can be helpful to create separate masks for each part of a characters body, such as a mask for the arms, legs, head, etc.

Transfer modes
This is pretty straightforward, but it is very powerful. To access the transfer modes, click the button at the bottom of the composition window that says "Switches/Modes". You now have the ability to set various transfer modes for a layer, which will alter the way that it is displayed on top of the layers below it. You can also turn any layer into a track matte here.

Motion Tracking
Motion tracking allows you to track the motion of an item, and apply the tracked motion to another layer. This is useful for replacing or covering up a part of the video. For instance, in my Smooth Criminal video, I used motion tracking to replace Michael Jackson's face with the face of Lupin. To do this I just used motion tracking to track the motion of Michael's head, then I applied this motion to a layer that contained only Lupin's face. This saved me the effort of having to animate the face manually. This probably won't be very useful for most videos, but there are times when it can really save you a lot of work.

Vector Paint
This is a feature that basically lets you paint on your video as if it were an image. Probably not too useful for most AMVs. Can be used for rotoscoping (frame by frame painting on the video).

Keyframe Assistants
The keyframe assistants allow you to easily manage your keyframes resulting in smoother animations. For instance, lets say you have an image drop down from the top of the screen. If you just set a starting keyframe off screen, and an ending keyframe onscreen, the image will just fly onscreen and suddenly stop. You probably want the image to slow down right before it stops. You can do this by right-clicking the ending keyframe and going to keyframe assistants and selecting "easy ease in". There is also a keyframe assistant for an exponential scale. When you scale an object normally, it will appear to grow/shrink at a faster rate when the scale value is small, but when the scale value becomes large, it will appear to be scaling at a slow rate. By selecting 2 scale keyframes and choosing the exponential scale keyframe assistant, it will make the scale appear to happen at the same speed throughout.

Parenting
Parenting allows you to apply the attributes of one layer to another layer. This can make it simple to have multiple layers interact with one another. For instance lets say you wanna make a solar system. First you can animate the earth moving around the sun. Now you wanna make the moon rotate around the earth. How are you going to do that though? Because the earth is always moving, it will be nearly impossible to keyframe the moon to move properly around it. By setting up parenting though, we can make the moon automatically rotate around the earth with a single click! How's that for convenience!

Shatter
The one effect everyone wants to use... It is capable of good, or evil. Use it wisely. A great tutorial on the shatter effect can be found on Creative Cow, right here.

Final Words
Now with this basic knowledge, you should have a solid foundation to learn how to do anything you want in After Effects. Sometimes it can be really difficult to get something to look how you want it to, but with practice and patience, you can achieve anything. Good luck!