Another great question. Not very well, basically. The guerrilla tactics caught the US off-guard, and to fight them they responded to some very heavy-handed tactics:

* They used their latest and most deadly bombing technology. Between 1965 and 1968 Operation Rolling Thunder was in effect, the goal of which was basically just to bomb massive swathes of jungle in the hope of taking out the Viet Kong who were hiding there. But it didn’t work very well. All too often they failed to hit the guerrillas, and ended up killing innocent civilians instead. This made the US look very bad abroad.

* They tried similar tactics on the ground, by deploying a pesticide called Agent Orange and also using napalm to wipe out the jungle and any guerrillas hiding in it. Again, this led to the deaths of innocent people – both from the flames and the poisonous pesticides – and also killed peasants’ crops, leading to starvation. This was intentional, because the US wanted people to be in the cities, which it had a better control over. Again, forcing innocent people out of their homes didn’t play well abroad.