Whole libraries have been written about the Vietnam War, and I will not try to condense them into a thousand words. There is a massive and bloody historical debate over what the "lessons of Vietnam" are, especially because the lessons seem to have such urgent policy implications in an era where the United States is fighting more wars that appear to superficially resemble it.
Everyone fights to avoid the blame for lost wars, and in the case of Vietnam we have even been subjected to the apparent absurdity of some people claiming that the war wasn't in fact lost at all, or rather, that the U.S. military didn't lose it, but the enemy just won it. The reason they won it, the reasoning goes, is because the U.S. civilian leadership wouldn't let the military do all they needed to do to win. This bears an eerie resemblance to Der Dolchstoß, the German army's "stab in the back" explanation for its loss in World War I, but it has a kernel of truth. A kernel. If I were to rail against my flatmates for not allowing me to burn down my flat to eliminate our rodent problem, I would have roughly as sensible a case.
Understanding this gets us to the heart of what went wrong during the Vietnam War. The root of the war was the North Vietnamese desire to unify the entire of Vietnam under a Communist government ruled from Hanoi. To achieve this aim, they needed to take over South Vietnam, which at the time was ruled from Saigon. The U.S. intervened to help protect the government in the South from the North's attempts to destroy it. What the U.S. did not ever try to do was actually to overthrow the Communist government in Hanoi by invading the North of the country, which would have addressed the root of the problem. Instead, with the exception of brief incursions, U.S. forces had to remain in the South and absorb wave after wave of attacks from the North, which came in the form of guerrillas infiltrated across the border and, later, full-scale conventional attack.
We are starting now to see the origins of the argument that if the U.S. military had been allowed a free hand, it could have won the war. And yet, there was a reason for these restrictions. Avid readers of Noung will know from my Korean War write-up that the reason the U.S. failed to achieve its goals in that war were because its invasion of North Korea sparked a Chinese counter-invasion; it was fear of a repetition of this event which kept American troops out of North Vietnam, for North Vietnam also borders China. The decision to forbid an invasion of North Vietnam was not just civilian squeamishness but a genuine fear of World War III against a nuclear China. China supported the Vietnamese Communists (although less than was thought in Washington at the time; they were more inclined to the Soviets), but even more importantly it did not want an American army anywhere near its border.
This restriction on what the U.S. military could do in Vietnam is one reason it was a "limited war", one fought under restraints. From the position of the military commander in Vietnam, these restraints may have appeared absurd and designed to stop him accomplishing his goals; but from the vantage point of the country's leadership, they were essential to protect other, more important goals (i.e. avoiding World War III).
Because they were unable to decisively invade the North and prevent it from continuing to attack the South, the U.S. leadership instead decided that it would try to destroy the political will of the North Vietnamese. The idea was to make them decide that actually national unification wasn't worth the hardship that the U.S. could inflict on them as they tried to pursue it. This strategy had a fatal flaw, which was that it ultimately required the co-operation of the enemy. If your strategy is to invade and destroy the enemy then he can be essentially passive in this process, but the U.S. strategy here required the North Vietnamese to react in certain ways. Their failure to comply - their failure to be cowed - was what doomed the strategy.
There were three prongs to the strategy. The first was the commitment of more and more troops to South Vietnam. The gradual escalation under the Kennedy and Johnson administrations was understood by the civilian leadership not primarily as a military action, but as a political one. When they sent more troops, they didn't do so because they had decided that more troops were needed to achieve military goals, but because they wanted to signal to the North that they were serious and committed. This misuse of troops to send a diplomatic message rather than to implement a serious military strategy typified the U.S. approach to the whole war. In fact, as the Vietnamese Communists well understood, the constant escalation placed such strains on American society that it appeared more as the desperate flailing of a drowning man than as a confident reassurance.
The second part of the strategy was the use of air power against the North. Through a series of bombing campaigns with names like Arc Light and Rolling Thunder, the U.S. tried to bomb the North so much that it would lose the will to continue. But the air campaigns never inflicted as much damage as Washington hoped, and the damage was never enough to do anything other than spark nationalist resentment and hatred of the U.S. This could have been predicted perfectly well by anyone who had studied the bombing campaigns that the Allies conducted against German cities during World War II. The bombings did not affect the capability of the North to attack the South, and they didn't persuade it to want to stop either.
The third part of the strategy, and one which resonates now because of the war in Afghanistan, was to build up the South Vietnamese state to the point where it could defend itself without American help. Because it was obvious U.S. forces could not stay in South Vietnam for ever, Saigon had eventually to be capable of looking after itself. It also should have been obvious that the U.S. could not coerce the North and destroy its will to attack the South for ever (in fact, it couldn't do this at all), so the South had to be capable of militarily standing up to the North. This was the only possible exit strategy for the U.S., and the only true definition of victory: the U.S. could repeatedly beat off Northern attacks, but if the North was only going to come back and finish the job later, then this couldn't be called victory.
And this is what eventually happened. American troops were gone by 1973, and South Vietnam was gone by 1975. Much has been made of the corruption, mismanagement and brutality of the South Vietnam regime, and it is obvious that the U.S. failed in its goal of establishing a durable regime there. It's worth remembering that the final defeat in Vietnam didn't come at the hands of pajama-clad guerrillas, but a full-scale, armoured conventional attack by the North; many people forget this, and hence exaggerate the potency of guerrilla warfare. The U.S. might have been able to protect the South against this assault with airpower and aid, as it had done against a similar attack in 1972, but it was Washington's political will that had been broken, not the North's. And even if this protection had been forthcoming, it would only have delayed the inevitable.
The U.S. error in Vietnam was primarily to ignore the type of war it was fighting. The Vietnamese Communists were incredibly committed to their goals, for which they had suffered immensely through decades of occupation and war. They could not be deterred by anything that the Americans had in their power to throw at them, because the Americans were constrained in what they could do by the wider strategic situation - China and the Cold War. As happened so often during the Cold War, the superpower conflict was the original cause of escalation and then also the factor that ultimately constrained it and made it limited. But while the war was "limited" for Washington, it was "total" for Hanoi.
America was committed to a war it could not win because policymakers failed to clearly recognize the nature of the war they were fighting. That so many had to suffer for something that was explicitly recognized as peripheral and of limited importance was the tragedy of Vietnam. The men who were drafted and sent to fight and die for a "limited" war had good reason to question their plight. Richard Nixon's response was to announce the Nixon Doctrine, which said that in future peripheral conflicts, the U.S. would expect its allies to provide the manpower for their own defence rather than expecting American boys to do it for them. This, along with the rest of his foreign policy of detente and moving closer to China, went a long way to restoring rationality and a sense of proportion to U.S. foreign policy; no longer would so many be asked to defend so little.