The Vietnam War was a watershed event in both America
n and Vietnamese History.
As pingouin pointed out, for Vietnam it was just a continuation of their ongoing war for independence. After being liberated from Japan at the end of World War Two, the Vietnamese turned to America to support their independence goals. However, France reasserted their colonial rule. This led to a guerilla war throughout the 50s, and France's eventual withdrawal. The newly liberated Vietnam was partitioned into two nations, a North Vietnam, led by Marxist Ho Chi Minh, who was the leader of the struggle against the French, and South Vietnam, an American puppet state with little public support.
The reasons for US intervention in Vietnam were tied to the cold war and fears of communism. The domino theory posited that if one nation in a region became communist, others would follow. While many have cited this as justification for meddling in the affairs of other nations, especially Vietnam, what gave the US the right to dictate an economic system for them? For some, there was the specter of Soviet influence gaining power, but not all communist nations were necessarily Soviet allies, for instance China and Yugoslavia. The idea of spreading Soviet influence may have been a mere scare tactic to justify intervention to prevent something the elites in the US really feared: an example of democratic communism being established somewhere. Indeed, a Ho Chi Minh led Vietnam was a likely candidate, given his admiration of the Founding Fathers of the US.
The war raged from the early 60s through 1975, with the level of US intervention escalating through the late 60s. The fighting was mostly a stalemate, the superior fire power of the US and US supplied South Vietnamese forces being balanced by the guerilla fighting tactics of the North and their allies in the south, the Viet Cong.
In the US there was considerable opposition to the war. Many opposed US involvement in the war because they saw it for the imperialist effort that it was. Others were total pacifists and still others simply did not want to be drafted to fight in it. All of these are valid viewpoints. There were serious confrontations in the US as the anti-war movement and other related leftist movements surged, including the Kent State Massacre.
Unfortunately, in recent years, this formidable opposition to the Vietnam War of a generation ago, in an Orwellian feat, has been rewritten mostly as opposition to the tactics of the war, and not the war itself. People lament about the folly of fighting an 'unwinnable' war, not about the folly of fighting an imperialist war to prevent a country's people from deciding their own future. Even an uncle of mine, himself a draft-dodger, now maintains the position that US policy was essentially correct, it was just the tactics of the war that were wrong.
Minorities and the poor were disproportionately drafted for the war. Initially local draft boards were responsible for providing a certain number of young men from their community, and naturally sent the ones whose parents had the least influence. Exemptions could be granted for everything from college to allergies. Later the draft was moved to a fairer lottery system.
As wrenching as the war was for the US, it was infinitely worse for Vietnam, which lost a million people. As the Nixon presidency continued through the 70s, the US engaged in massive bombing campaigns against the North as well as deforestation campaigns with deadly toxic agents such as Agent Orange that devastated civilian populations. Under Secretary of State Henry Kissinger, himself a survivor of the Nazi Holocaust, the air campaigns were carried to civilian areas of Laos which were supposed to be bases of operation for the Viet Cong.
The US gradually withdrew troops in the 70s, and ended operations in 1975, officially with the war being a stalemate, but evacuating personnel from Saigon as North Vietnamese troops were entering the city.
In the US, healing from the war was gradual, with president Carter pardoning all who had evaded the draft, and the Vietnam Memorial being completed in 1982. Vietnam was a country devastated and has not recovered to this day. The regime of Vietnam has for the most part embraced capitalism in recent years.