I suppose the best answer to this is that the French started the Vietnam War right after World War II.
Vietnam had been a colony of France. It was taken away by Japan during the war. Some Vietnamese fought to become free from Japan. After the war they wanted to be free from France too.
France didn't want them to become free so they fought the "Vietminh" who were the Vietnamese (communists) who fought the Japanese.
Our involvement in the war started when we supported the French. When they lost and left the country in 1954, we took over.
Our really heavy involvement in the war didn't start until 1964 when Lyndon Johnson used the Gulf of Tonkin Resolution to start putting lots of American troops in. We got in because of our fear that communism would spread if the communists took Vietnam.
Although most wars have a definitive beginning, such is not true with the Vietnam war. American involvement began in 1950 when President Harry Truman okayed economic and military aid to France, who were fighting communist takeover attempts in their former Indochina colonies. The French loss at Dienbienphu, Vietnam in 1954 gave the communists control of the northern part of the country. Shortly afterward, President Dwight Eisenhower ordered military advisors and CIA operatives to set up a U.S. backed government in the south.
President John F. Kennedy sent a Green Berets force to further train the southern army in 1961, and by late 1963 there were more than 15,000 American "advisors" in Vietnam. Following Kennedy's assassination, President Lyndon B. Johnson added the first formal troops when he sent in a large Marine detachment. Johnson later ordered bombing in the north by American aircraft, and soon the undeclared war escalated even further.
Vietnam was initially under French control. Following the German’s defeat of France during World War II, France fell into an alliance with Japan. The Japanese were gaining control over Vietnam, Laos, and Cambodia through their allegiance with France. The Vietnamese became concerned about their own well being. The Viet Minh retaliated against the French and Japanese and led a rebellion of the people. Ho Chi Minh, the leader of the Viet Minh, declared leadership of the country. The United States and other allies supported that the country belonged under French rule. France began efforts to take back power over Vietnam. French troops overthrew the city of Hanoi dispersing the Viet Minh. The Viet Minh began guerilla assaults leading to the war now known as The Vietnam War..