And how did this technique have such an effect?
Guerilla warfare was their best friend. It only took a couple of Viet cong to lay traps ranging from spike pits to tripwire explosives. One exam Olen of these treasures was that the VC would put a grenade in a soup can (or something similar) and tie a string to the pin, white the other end tied to a tree. The soldier would pull the string, releasing the pin and causing an explosion. The problem was these attacks came seemingly out of nowhere, and created an illusion of the jungle being against the US. These tactics are a large factor for why PTSD cases from Vietnam veterans was so high, the US were fighting an enemy they couldn't see.
So, guerilla tactics were the most effective against US morale to answer your question. BTW, this wasn't the first time guerilla tactics were used. Medieval Welsh Scottish and Irish resistance was usually led in guerilla form as they weren't as well equipped as their English enemies. Obviously grenades weren't used, but it was the same trap and ambush tactics that define guerilla warfare.
Hope this helps! I'll try and answer any further questions if you've got any.