Triggered abilities are not played or cast, then automatically trigger when their trigger condition is met. Because of this, there is not a cost to have these abilities trigger. However many trigger do have costs associated with them when they resolve.

This matters with cards like Kuldotha Flamefiend from Mirrodin Besieged. The Flamefiend’s ability triggers when it enters the battlefield. This trigger then goes on the stack after the Flamefiend immediately after this, no other costs need to be paid. When this trigger goes on the stack the controller of the ability will choose the necessary targets. (In this instance, it can be from one to four target creatures or players.) At this point both players will receive priority and can play other spells and abilities. It is when the Kuldotha Flamefiend’s triggered ability resolves that the controller of this trigger can sacrifice an artifact. If he does, then four points of damage will be dealt to the chosen targets. If he does not, then nothing else happens.