The important things to remember are:
- A trap has two parts: the trigger and the result.
- Each part must be detected separately, and may require different search methods.
- Search order is important; one method may find a trigger, another method may trigger it.
There are a couple very basic triggers, but these can be chained (the result of Trigger A is the triggering of Trigger B.) They can also work in parallel (a lever in Trigger A moves two other levers simultaneously, triggering Triggers B and C.) Sometimes Trigger A disengages Trigger B, making another action safe, so finding a "trap" and avoiding or disabling it is not always a good thing.
Results can be pretty varied, but they can all be simplified to an action delivered along a particular path, from Origin Point A to Target Point B. A character standing at the target point or along the path between the origin and the target is in danger of being caught in the trap. Examining Point A may locate a trap, but not its trigger; examining Point B may offer clues to what kind of result to expect (scorch marks on a wall are a clue to a flame thrower trap, debris on the floor may be a clue to a deadfall.) Some results, like releasing a gas, might not be obvious from any kind of clue.
When constructing a trap, you should consider both obvious actions (walking over a trapped floor, opening a trapped door) and search methods (touching or moving a trapped chest.) Sometimes, a particular search method will trigger the trap, which might not be a good idea based on whether you are standing in the path of the result or not.
Consider this simple setup: you have two parallel corridors connecting two locations. In each corridor, there are two adjacent pressure plate triggers, each one the width of the entire corridor, so that people walking down the corridor first step on one trigger, then the other. There is no normal way to jump over the triggers (the distance is too great,) but magic could avoid them. One trigger disengages the second trigger in that corridor while pressure is applied and for one round after it is released; the second trigger, if pressure is applied when it is not disengaged, causes something bad to happen.
The result of this setup is that walking normally down the corridor in one direction is safe, while walking in the opposite direction triggers the bad result. You now have a one-way corridor. The parallel corridor has the same setup, but with the opposite direction; the inhabitants of the dungeon know to use the left-hand corridor, whichever direction they are headed (the parallel corridors could, of course, be merged, and the inhabitants would walk single-file along the left-hand side, much like road traffic in the U.S.)
A visual search of a "one-way corridor" could find both triggers, but that doesn't help the adventurers figure out that what matters is the order the triggers are stepped on. Using a 10-foot pole to press Trigger A (which disengages the trap) does nothing visible; pressing Trigger B within one round of pressing Trigger A will also do nothing visible, since the trap is disengaged. At this point, a party of adventurers may decide there's no danger and continue down the corridor, which might have no effect if they are heading the right direction. It's when the now-inattentive party returns down the same corridor when the problems begin.
I've got more specific things to say about each kind of trigger later.