Okay, I've got a few minutes, I'll give you a few basics. Triggers, basically, make things happen in a scenario. They can be any number of things from displaying messages (dialogue), killing objects, creating objects, tasking objects, changing diplomacy amoungst players, etc. (These are all effects and they are pretty self-explanatory) These effects are set-off a number of ways. Either they can be active the moment the scenario starts, or they can be activated by another trigger or they can have a condition that activates them. Conditions are usually required in a trigger but not always. You might have a trigger where you want to display a message after a certain building is destroyed. This would have a condition of destroy object (the building) and an effect of display instructions "Hey, that was my house!!" You might want to have a player change diplomacy when they arrive at a gate. This would have the condition of bring object to object (character to gate) and an effect of change diplomacy (player 1 ally with player 2). One more example might be you want to create a small army to attack you when you reach castle age. The condition would be research technology (castle age) and you might have several effects, each one creating enemy units just outside your line of sight. You might also have another effect that activates a second trigger that would task all these units in that area to move to your base and therefore a battle would occur (as long as both players diplomacy was set to enemy) Are you beginning to get the idea? There are loads and loads of possibilites with triggers depending on how you activate them. I use activate trigger effects an awful lot.
To do all this wonderous stuff, you simply create a new trigger under the trigger menu and set the options for that trigger. Give the trigger a name to help you distinguish which it is. You can have the trigger on or off depending on whether you'll activate it later with another trigger. You can set the trigger to be an objective of the game like "Destroy Monastery" in which case it would show in the objectives window at the top of the screen (be sure to name it correctly) and it would be crossed out once the building is destroyed. You can set the trigger to loop which means it will continue to run for the entire scenario unless you deactivate it with another trigger. This is helpful if you wish to continue creating units throughout the game.
I hope this has helped a little. If you have a question about a particular condition of effect in a trigger, it's really easy to create a scenario and test it. I do this all the time, especially if the trigger is complicated or has some timer based conditions that need to be refined. Good luck......