How did the United States become involved in the Vietnam War?
US involvement was more complex than this.
The US had been involved in Vietnam before the end of World War 2. At that time Vietnam was part of French Indo-China along with Laos and Cambodia.
With the defeat of the Japanese in 1945, the French assumed they would resume where they had been in 1945. However the Vietnamese fought the French and under General Giap defeated them at Dien Bien Phu. At a peace conference in 1954, Vietnam was divided into 2 at the 17th parallel, communist North and US backed south. Cambodia and Laos were declared neutral.
In the South the US backed President Diem was supposed to hold elections but refused to do so. Opposition mounted and violence increased. The US increased military aid but to no avail. In 1963 Diem and his brother were assassinated by a CIA backed military coup. Shortly after Kennedy was assassinated and US involvement escalated under Johnson.
Despite huge amount of men and money the Americans could not secure victory and in 1973 pulled out. Within 2 years all of Vietnam, Cambodia and Laos was under communist control.