Hmm... I'm not the greatest teacher, but here's some visuals...
This is the setup for basic automation of a Live Input...

That's for basic 32nd-note gating of a Live Input. You can go much further by automating FX too. Some uses i've found:
1) Pan your voice around the room while you're on the mic...without having to turn any knobs
2) Mic the crowd and have the crowd sound swell in and out with the beat
3) If you're playng a synth or on the mic, you can have the last beat of every two measures sent to a Return Track for echo.
4) Run turntables or a CD player into Live and automate FX on it
5) For audio/visual stuff : run the sound from your video clips/DVD into Live and automate FX/volume on that. We've had lots of fun remixing movies in realtime using this technique
and this is the setup for peeddrroo's super crossfader trick
It's late and i'm very tired...hopefully this is helpful...i'll work on it more tomorrow...