The history of the Vietnam War goes deep into the past, but the modern era began with the defeat of the Japanese after World War II. The French attempted to reassert their pre-war colonial power in the region, backed by the U.S. but failed after a painful nine year struggle that ended with the Geneva Accords of 1956 and partition of the country. The peace of those accords was an illusion and soon Communist forces backed by Ho Chi Minh's government in North Vietnam were at work attempting to undermine the regime in the South.
Ultimately the U.S. was drawn into a major commitment to the defense of South Vietnam, compelled to do so by the region's history and by the need to oppose further Communist gains in Asia. The escalation of the war on the ground in Vietnam, over adjacent borders, and with a major bombing campaign did not defeat the Communist forces but did suppress their efforts and gave the South Vietnamese time to build their own army and gain the ability to defend themselves. However, as the South Vietnamese successfully dealt with the internal Communist Viet Cong insurgency, North Vietnam increasingly took over conduct of the war as a conventional invasion by outside forces.
Ultimately, the U.S. withdrew under the pretext of a new agreement with North Vietnam signed in January 1973, forced to leave prematurely by political pressure on the home front that undermined U.S. ability to vigorously prosecute the war. North Vietnam had agreed not to increase its strength in the South, but in December 1974 North Vietnam invaded and the U.S. did not intervene. ARVN, the army of South Vietnam, initially fought hard but were overwhelmed. Saigon, the capital of South Vietnam, fell in April 1975 allowing the Communists to control the entire country. Neighboring Cambodia and Laos fell to Communist forces in the same year.
These pages of Olive-Drab.com develop the history of the Vietnam War in more detail: