The US became involved in the war after the most powerful leader in Vietnam, Ho Chi Minh, took support from the communists.
Ho Chi Minh had previously defeated the French after they tried to force a government on the people of both North and South Vietnam.
After the French were defeated, the country was given an election to determine if they would be a democracy or communist and the communists won. The US would not allow another nation to fall under control of communism and so, after considerable political pressure, Vietnam was divided in two.
In the early 60s, North Vietnamese operatives began to raid the south and it became increasingly difficult for the Vietnamese to hold them off. The US created the Green Berets in order to train the locals how to defend themselves, but it still was not enough.
In 1965, President Johnson (the man who replaced JFK after he was assassinated) sent a considerable force of troops to south Vietnam in order to protect them.
Even with US forces in Vietnam, the Communists were almost completely free to do what they like in the North, and so an increasingly large US force was required. Eventually over 600,000 US troops were stationed in Vietnam at any one time.
The US placed restrictions on their own bombers in order to try and wear down the north without actually taking over the country.
The US dropped far more bombs than were dropped in all of WWII, but because there were massive areas of North Vietnam that were off limits, it was ineffective.
In the late 60s there were several massive offensives by the North, such as the "tet" offensive. The North threw men at the South in huge numbers and the US repelled and killed tens of thousands of enemy troops.
In military terms the US was extremely sucessful, losing "only" 58,000 for the 1.8 million+ North Vietnamese which were killed.
In political terms, the US lost, simply because its military came across as a bully who was killing everything in site.
The media was a significant factor in the political loss of the Vietnam war, since it has been proven that a good deal of reports by all sources were false or biased.
For instance, there is a picture which enraged the US, a picture of a South Vietnamese police chief executing a North Vietnamese insurgent. The picture was taken the instant the gun went off.
The media made it seem that our allies were just ging around blowing people's heads off, but the truth was completely different.
The insurgent who was executed had just murdered an entire family, and even to this day the cameraman stands up for the police chief and is even friends with him.
It was things like this which made a waste of the 58000 US lives and hundreds of thousands of limbs lost in Vietnam.
Towards the end of the war, the US forces under the command of President Nixon made huge strives toward crippling the north. Massive bombing campaigns like operation rolling thunder II leveled every major North Vietnamese military installation on the surface.
In the early to mid 70s, the US and the North began peace talks. The US had almost completely crippled the North as of 1973, and so in 1974 a peace treaty was signed.
The North was reduced to about 1/5th of its strength, and the South was left with a huge modern military funded by the US, but after the US pullout, the South's economy collapsed and it could not longer support its military.
In 1975, the South collapsed, and the North rolled in with a relatively small military compared to what it previously had. The South's military ran, and was trapped in the congestion caused by fleeing civilians.
The Northern Army surrounded the Southern Army at a bottleneck in a major road and killed over 250,000 soldiers and Civilians.
From there on the North was almost free to do whatever it liked.
Eventually it took all of South Vietnam, and they became modern Vietnam.