The war started because the Communists in North Vietnam wanted to overthrow Western Colonial Powers and the USA and France wanted to stop the spread of communism. After the French were defeated, the USA gradually increased the number of troops during the 1960s.
Operation Rolling Thunder
The Geneva Accords, in 1954, divided Vietnam into the Communist North Vietnam and the Republic of South Vietnam. The Communists were unhappy and immediately began creating militias in South Vietnam to fight the government there.
North Vietnam attacked 2 USA ships in the Gulf of Tonkin. The USA Congress gave the President the power to wage war against North Vietnam in the Gulf of Tonkin Resolution.
The End of the War
Operation Rolling Thunder was a massive bombing campaign by the USA against North Vietnam. The United States dropped more bombs on North Vietnam than were used during all of World War 2.
In 1968 the North Vietnamese attacked cities all across South Vietnam on the lunar New Year holiday called, Tet. The North suffered many more casualties, but the attack showed that the USA was not close to winning the war.
The USA withdrew the last troops from South Vietnam in 1975. The Communists soon overwhelmed the South Vietnamese and conquered all of Vietnam.