How do TV-Based Video Game Guns Work?

mark juncosa asks: "It is a mystery to me how Nintendo's Duck Hunt gun works. I have thought about it for a long time and have not been able to come up with any kind of good solution." Come to think of it, I wouldn't mind knowing this one myself. On a guess, I'd say that the system is entirely active and all the work being done by the gun and the TV remaining the display device that it always has been. Am I close? Or completely off base?