Why did the U.S. become involved in the conflict in Indochina?

The short answer to this question is that policy leaders in the United States feared the spread of communism. Operating under a concept often described as the "domino theory," they thought that if Indochina, and after the overthrow of French colonialists South Vietnam, fell under communist control, the path to communist dominance in places like Thailand, Indonesia, and even India would be opened. The United States initially supported France in its struggle against the independence movement in Indochina, and when the newly-free nation was divided by the Geneva Accords, the support for anti-communist South Vietnam against communist insurgents backed by communist North Vietnam continued in the form of military "advisers" sent by the Eisenhower and Kennedy Administrations. But the struggle against communism faltered, and when the US-backed South Vietnamese leader Ngo Dinh Diem was overthrown and assassination (with some US complicity) the country descended into civil war. The true military buildup began in 1964, when an attack on American destroyers off the coast of North Vietnam became a pretext for the Tonkin Gulf Resolution, which authorized President Lyndon Johnson to use whatever force he deemed necessary against North Vietnam. Johnson authorized a bombing campaign, and when Vietcong forces attacked American airbases, he began a steady military buildup that poured American troops into the conflict. By 1965-66, the United States was fully committed to the conflict.