A short history of the Vietnam War with an emphasis on American participation there.
Indochina (which is currently Vietnam, Cambodia, and Laos) was a French colony since the 19th century (they acquired it in pieces between 1858 and 1884). When France was conquered by Germany in June 1940, Japan figured that Indochina was vulnerable and conquered it in September 1940. When Germany and Japan were defeated, France re-established control.
Meanwhile the people who lived there were never really happy about the situation and had been an active resistance movement against France (and Japan) pretty much since 1858. France had been weakened by World War II and was not able to keep control of the country. Their last major military effort was ended by the defeat of the French forces at the Siege of Dien Bien Phu in 1954.
By this point, the Vietnamese resistance movement had been unified into a single organization called the Viet Minh which was led by Ho Chi Minh. The group contained all the factions that were opposed to French rule but its largest group were the Communists (as was Ho himself).
After Dien Bien Phu, there was a meeting in Geneva between France and the various Vietnamese resistance groups. Vietnam, Laos, and Cambodia were recognized as independent countries and France agreed to withdraw its troops.
Vietnam was a special case because the country was not controlled by a single group. The Viet Minh, which were now controlled by the Communists, were in control of the northern part of Vietnam and various non-Communist groups were in control of the southern half of Vietnam. As a temporary solution it was decided to let each group keep control of the half it currently had with an election scheduled for 1956 to decide who would be the government for Vietnam.
The United States had provided support to France while it was fighting but had not been directly involved. But after the Geneva Accord it was clear that the 1956 election was going to turn Vietnam into a communist country (there were more people in the north so they would outvote the south). So we encouraged Southern Vietnam to declare itself a separate country which it did in 1955 as the Republic of Vietnam. The northern half, which called itself the Democratic Republic of Vietnam, did not recognize the independence of the southern half and began working to overthrow the southern government. The Republic of Vietnam obviously fought back against this and President Eisenhower sent American troops to act as military advisors to assist the southern forces in 1955. Under Eisenhower, there were about 700 American troops in Vietnam.
When Kennedy was elected in 1960, he expanded support to the Republic of Vietnam, sending more money and more troops. By the time he was killed in 1963, there were over 16,000 American troops in Vietnam.
When Johnson took over after Kennedy’s death, he felt he had to maintain Kennedy’s commitment to Vietnam. He sent more troops raising the total to around 21,000. But the big jump came in August 1964 when Northern Vietnamese ships allegedly fired on American ships in the Gulf of Tonkin. Congress passed the Gulf of Tonkin Resolution which gave Johnson the authority to commit whatever forces he thought were necessary to Vietnam to protect American troops there and to defend the Republic of Vietnam. Johnson interpreted this authorization widely and by the end of his term in 1968 he had increased the number of American troops in Vietnam to over 500,000. This made Johnson very unpopular and he decided not to run for re-election in 1968.
Nixon won the election in 1968 by, among other things, promising to end the war. He took a few detours along the way (including sending more troops and invading Cambodia and Laos) but the Paris Peace Accords ended American participation in the war in January 1974. Following the American withdrawal from Vietnam, the Republic of Vietnam was unable to defend itself and was overrun by the Democratic Republic of Vietnam in April 1975.