Tip #1 - Shortcuts
I mostly work with Shortcut keys to speed up my work. Here a small list of those I use most.
Tip #2 - Composition Size
Always work with a broadcast sized composition. If you do your work on a too small composition you will not be able to resize it without loss of quality.
It's always easy to downsize it.
Here some Standards:
Tip #3 - Audio Format
After Effects has the capability to import mp3, wav and wma. But I would rather go for the aiff format, it's fast and there is no loss of quality. Even on a windows system use aiff. The decoders in aftereffects for mp3 and all the other soundformats are very slow.
Tip #4 - Naming
Give your Compositions and layers names. Names are very important! If you are working on a big project, let's say more than 30 layers, then it's very helpful when you know where is which piece of film.
Tip #5 - Alpha Channels
Never underestimate the power of AlphaChannels, they can help you a lot when you don't know any further.
Tip #6 - 3D
From AE 6.x upwards you have the possibility to move in a "fake" 3D space, you can do a lot of stuff with it, Just click the small Cube ticker on a layer, and you can now change the Z axis of a layer
Tip #7 - Camera
3D effects are pretty cool, but don't forget that your camera is already in a 3D space, instead of animating 100s of layers, animate your camera.
When working with cameras, don't forget to switch your workspace to "Two Comp Views"
Tip #8 - Memory
Get LOADS of RAM.. After Effects stores any rampreview any slidescrubbing you do into your RAM, if you have enough of them then you will be fine, otherwise create a big pagefile, and give Aftereffects at least 65% of your memory.
Tip #9 - Effects
Don't pile up effects on one layer only, this is not photoshop!
Rather try to create every single piece on a new composition and at the end put all them together.
Tip #10 - PLAY
My favourite tip is PLAY WITH AE, really you can do whatever you want, I always get the most stunning effects, when I play around. Every effect has 100's of settings, you will never learn them all. So get a few bottles of coke and just have fun.