Welcome to our nightmare, gunner!
I take it you mean a semi-auto pistol? Well, there are several different systems in use by manufacturer's and each one is a bit different than the others. The simplest system uses a lever that is attached to the trigger on one end and that firing pin block on the other. When the trigger is pulled it retracts the lever and pulls the block out of engagement with the firing pin. This set-up is timed so that the block does not completely clear the firing pin until the trigger is pulled fully to the rear. This, of course, is an oversimplification of the system and not totally accurate, but it gives you an idea of how the basic system operates. Hope it helps.