How did the Vietnam War start?

It started on November 1, 1955 for the Vietnamese . It would be six years before the U.S. put (non-advisory) troops there.

In short, the U.S. intervention in Vietnam was inspired by "Containment Theory." American officials feared that the more Communism spread, the more difficult defeating the Soviets would become. Ideology would bind Communist nations together, just as "Liberalism" had, in their eyes, bound the Allied Powers. However, history is often distorted by oversimplification. In truth, the Vietnam War was influenced by French Colonialism, Communist provocation, dictatorial rule in the South, and U.S. quasi-militarism.

The Vietnamese people were split. North Vietnam was being taken by Communist influence, China and the U.S.S.R., by proximity and interaction, was "infecting" the French Indochina with their doctrine. The Vietnamese felt alienated by colonial influence, the area suffered from poor production and a low standard of living. Communism seemed to Vietnamese, under the leadership of one Ho Chi Minh, a birth of equality and prosperity for their ailing people. To the Americans, however, it was a plague.

This validated Kennan's grounds for "Containment Theory" (if this is for APUSH, remember George C. Kennan!), and as such, the U.S. moved to quarantine Communism in Asia. The U.S. sent military advisors to prop up the Southern Vietnamese dictator Diem and make a "wall" against which Communist influence would fail. This seemed to be a fair plan, except two things worked against it: Doctrine didn't necessarily move strictly physically, and Communism as a thought pattern took (a lighter) hold in the South as well. Further, Diem was hated by his people for his violence he alienated South Vietnam.

At that very moment, the U.S. was pulled into the quicksand of a "War of Containment." Without Diem, more support was needed to prevent Communism from spreading Southward. The U.S. begins mobilization of soldiers and the Americans in Vietnam grow exponentially. By 1964, the U.S. authorizes military action in Asia through the Tonkin Gulf Resolution, not a declaration of war.