There were two major differences between Korea and Vietnam. S. Korea is surrounded by water on 3 sides, so there could be no communist infiltration from the west, as happened from Cambodia into Vietnam. And there was no S. Korean version of the VC. So this war was, at least, a conventional one.
How to win in Vietnam? Well, to start with, you have to take a 'damn the torpedoes' approach, and not care if China gets in or not; then invade the north, maybe bomb Hanoi and Haiphong to death, cause a Tokyo-like firestorm, make them think that it just isn't worth trying to get the south back. You still have the VC, but without the north, they gradually wither, until they are just a nuisance. Of course, to do any of this, you have to have a president, and a large portion of the Congress, who doesn't give a shit about world opinion. They need also to put the fear of God into Red China, to keep their asses out of it, and also to use some sort of carrot and stick tactic on South Vietnam, to make ARVN effective, instead of an army that was full of gutless cowards, as it was in OTL.