After the Geneva Agreement, the USA became more and more involved in South Vietnam because they feared that it would be taken over by communists. This was because Diem’s government was incompetent and deeply unpopular. It was hated by the Buddhist majority in Vietnam because:

He favoured the Catholic minority and persecuted Buddhists
He crushed opposition brutally
Land was taken from peasants and given to Diem's supporters

This led to dramatic protests, for example when the Buddhist monk Thich Quang Duc burnt himself to death in 1963. In contrast to Diem, Ho Chi Minh carried out land reform in North Vietnam and was popular.

Opposition to Diem led to the US sending money to support the government of South Vietnam and special advisers to train the ARVN (the army of South Vietnam). At first there were 17 advisers in 1954 but this rose to 685 by the time Eisenhower left office in January 1961 and 16 000 when Kennedy was assassinated in 1963.

In 1960 Vietnamese communists started the NLF (National Liberation Front) which became known as the Viet Cong. By 1961 they had nearly 100 000 members and were murdering about 4000 government officials a year. The Kennedy government tried a policy of strategic hamlets (moving peasants into secure villages with schools and medical centres) but most were not safe from the VC and the policy was very unpopular. In 1963 Diem was assassinated and South Vietnam fell into further chaos.

A letter left by Thich Quang Duc before his self-immolation:

Before closing my eyes and moving towards the vision of the Buddha, I respectfully plead to President Ngô Đình Diệm to take a mind of compassion towards the people of the nation and implement religious equality to maintain the strength of the homeland eternally. I call the venerables, reverends, members of the sangha and the lay Buddhists to organize in solidarity to make sacrifices to protect Buddhism.

GCSE Conflict in Asia 1950 - 1975 AQA

How the USA became involved