The screen flashing when you clicked the trigger was the key. Also calibration of the light gun was imperative to it working right (having to point to the four corners and pull the trigger).

The process is actually quite deep. I will have to find one of the better articles on how it worked. The basic idea is the screen flashing when pulling the trigger, it would produce a white box around the duck and if calibration was correct and your aim decent then it counted as a hit.