Between 1946 and 1950, the French fought the Viet Minh with little direct help from the U.S., however, when China fell to the communists in 1949, and North Korea invaded South Korea in 1950, the U.S government became afraid of the communists taking ultimate power over Asia. Yet, with the U.S. involved militarily in Korea, they had to let the French do the fighting against the communists in Vietnam but the U.S began to support the French more and more. By 1954, the U.S. was giving France over $1 Billion a month to help in their fight in Vietnam. It was a losing battle. The French were fighting a people who were fighting for their freedom, for their independence, and the French eventually lost. In 1954, after the decisive French defeat at Dien Bien Phu, the French finally surrendered. In the peace treaty that was signed in Geneva Switzerland in 1954, called the Geneva Accords, France agreed to gradually remove all their troops from Vietnam.
The U.S. by this time, however, was not willing to accept a French surrender that would mean that another Asian country would fall to the communists, so they agreed to not fight on the basis that the Americans took responsibility for the southern part of Vietnam while the Viet Minh took responsibility for the northern part. Originally, the Geneva Accords, recognizing that there were two completely different political systems involved (communism and capitalism) stated that the communists would be allowed to consolidate their positions in the north and the capitalists would do the same in the south. Then, in two years, in 1956, there would be a national election that would determine what form of government the entire country would have. In effect, the Geneva Accords gave both sides a two-year breathing spell. This two-year period though, proved disastrous for Vietnam. The U.S. backed government in the south (not a national government yet, just a bureaucracy to take care of necessary business) refused to sign the Geneva Accords (France and the Viet Minh did). Thus, because they did not sign, the southern Vietnamese leaders felt (with U.S. encouragement) that they were not obliged to live up to the terms of the Accords.
Then, with U.S. military and economic help, a U.S. picked southern Vietnamese leader, Ngo Dinh Diem, assumed the leadership of a U.S. sponsored Republic of Vietnam The U.S. even wrote the constitution for the new "country." From 1956 until his assassination in 1963 (just weeks before John F. Kennedy's assassination) Diem ran South Vietnam as a tyrant, with the U.S. backing his every move. The U.S. also kept increasing the numbers of U.S. servicemen serving in South Vietnam, ostensibly as "advisors" to the South Vietnam Army . These numbers rose from a few hundred in 1956 to over 15,000 in 1963. The Viet Minh had won the war. Ho Chi Minh spent most of the period from 1954-1959 consolidating his hold on North Vietnam, all the while hoping that the international community would force the South Vietnamese and the Americans to live up to the Geneva Accords.
When this didn't happen, he, first, encouraged the communists still living in SVN to actively combat the Diem government. This was the start of the guerrilla war in South Vietnam with the southern communists, Viet Cong, fighting the ARVN troops. Americans were not yet involved in the day-to-day fighting except as advisors. In 1959, North Vietnam started infiltrating Northern Vietnamese Army troops into South Vietnam.
And the government of South Vietnam started to fall apart at the seams. To keep the south Vietnam government from collapsing, the U.S. had to keep increasing its aid to SVN. When his own generals in a coup assassinated Diem in November 1963, South Vietnam was very close to falling to the Viet Cong and NVA forces. In short order, the U.S. government decided that if South Vietnam was to be saved, it would have to be done through the use of American troops, thus, in March, 1965, Lyndon Johnson sent the Marines into South Vietnam, which began our military part of the war.