whatever happened to the nice document ENworld hosted that explained AoO's clearly.
It ain't bloddy rocket science.
Movement AoO:
If you LEAVE a threatened square, you trigger an AoO.
If all you do is Move that round, you negate the AoO.
Doing Stuff:
Casting, tripping, grappling, changing items while in a threatened square can trigger an AoO.
If you have the right feat or make the right skill check, you negate the AoO.
Did I miss anything? The Doing Stuff one covers all the side activities (if I missed an activity, it's still the same rule).
For a GM, the easiest way to retain AoO, and reduce the worry, is to ALWAYS assume everybody takes the optimal path. If somebody says, I go over here, and fight this dude, assume they used movement mode and path that triggers the least AoOs. Don't be a jerk about "you didn't say you avoided that guy that you clearly had enough movement to avoid."
AoO rules are in place to add realisim "aka danger when you do stupid things in front of an armed opponent". Walking away from the enemy, changing weapons, casting spells, etc would be stupid things to do while standing within swords reach of the enemy. The "Leaving a threatened square" rule is in place to cover running past enemies, and trying to leave a fight, both things the enemy would surely try to take a swing at you for (and possibly justify an extra swing in a real fight).
If you're DMing for newbies, you don't even have to fully explain AoO's. Just say, if you do something risky while facing an enemy, he may get a free attack against you. If the player is about to do something that would generate an AoO, tell him, if you do that, the enemy will get a free Attack of Opportunity. And be sure to throw in a few risky acts by the monsters, so the players see it goes both ways.
If your players don't do stupid things in combat, you'll never see an AoO. Honestly, I think I've had 2 AoO's rolled against me in 6 years of gaming in 3E. They simply don't come up that often.