In 1954 Ngo Dinh Diem returned as Prime Minister for South Vietnam and in 1955 he declared South Vietnam a republic and refused to hold the 1956 elections that had been decided in Geneva, seven years earlier. He was supported by the U.S. (who also completely ignored the Geneva Peace Convention) who were supposedly Democratic but only because apparently if the elections had gone ahead over 80% of the populous would've voted for Communist rule, which was what the U.S. had been trying to prevent in the first place. Throughout the following year, communists who had gone North began to return to the South in vast numbers, they were known as the Vietcong. They began to attack U.S. military bases that had been established in South Vietnam in 1959, and they began to use their Guerilla tactics against the Diem government, In 1960 their attacks began to grow and North Vietnam declared that its aim was to 'liberate South Vietnam from the ruling yoke of the U.S. imperialists and their henchmen.' After accusations were set that regular North Vietnam troops were taking a direct part in these attacks the Vietcong set up their own political group, called the National Liberation Front to prove that they were indeed independent.
In 1961 President Eisenhower left office and was succeeded by President John F. Kennedy. He sent a further 16,000 'military advisors' to Vietnam and set up the 'safe village' policy, which was conceived to try and isolate the Vietcong by moving entire villages into fortified hamlets, thus cutting off the Vietcong. The policy failed though, as the majority of the Vietcong were peasants anyway and continued their activities inside the hamlets. After Kennedy's assassination in November 1963, re-elections took place and Lyndon Johnson won after the American public favoured his more cautious approach compared to Goldwater's over the top 'We'll kill 'em all' policies. Johnson maintained the same policy of Kennedy's force of advisors but knew he would have to justify America's involvement in Vietnam.
Also in November 1963, the much hated Diem was overthrown by a military coup and assassinated. Over the next 18 months ten different governments were elected but not one could deal with the situation and in 1965 General Thieu and General Ky created a more capable council. Finally in 1967, Thieu was elected President of South Vietnam.
In 1964 there were reports that two North Vietnamese patrol boats had attacked a U.S. naval ship. This lead to a much deeper involvement in Vietnam by the U.S. after it caused so much outrage to the American public. This gave Johnson the excuse he needed to launch a full blown attack on Vietnam. He asked congress if he could increase military involvement and by the end of 1965, 200,000 American soldiers were in Vietnam. The Vietcong launched an attack on an American special forces camp at Pleiku, which led to America's retaliation of 'Operation Rolling Thunder.' This operation involved the first air raids on Vietnam since the beginning of the war, they were halted in December in a vain bid for peace, but this failed and so the raids continued.
In 1968 General Giap, a North Vietnamese strategist launched the TET offensive. This involved the Vietcong launching fierce attacks on over 100 urban targets in hope it would bring South Vietnam to its knees. Despite the emotional distress it caused to many people, it was not successful enough and ended in the Vietcong losing 80,000 fighters and being driven back to North Vietnam with only a few positions gained in the fighting left.
Back in the U.S., many Americans were beginning to oppose the war as they began to realise that this was an un-winnable war. In 1970, at Kent State University in Ohio, 4 students were shot and 9 were injured by National guards during a protest. In 1971, several papers including the New York Times claimed to have found government documents which cast a dismal light on the way the U.S. were handling the Vietnam situation. By this time, President Johnson was now avoiding public appearances for fear of his life, due to the bitter public opposition to the Vietnam war.
The main reason why the U.S. felt it so necessary to get involved in Vietnam was because they were so terrified of the 'Domino Effect' coming true. They wanted to stop the spread of communism at all costs, but only after over 2 million people were killed and more than 3 million were injured. Most of these lives were those of innocent Vietnamese civilians. And also the effects of chemicals such as Agent Orange and Napalm are still affecting the lives of the Vietnamese today, their land is contaminated, along with there water and food supplies. More bombs were dropped on Vietnam by the Americans than were dropped in the entire WWII, which perhaps really does prove the U.S. were really ready to do anything to prevent the 'Domino Effect' from becoming a reality.
There are other factors as well, the French were great allies to the Americans during the Cold war and it was really expected of the American's to move in on Vietnam. There was also SEATO which stated that the American's had to prevent the spreading of communism. With Vietnam being such a small country with primitive technologies, how much opposition could they be against a super power like the Americans? Apparently quite a lot. President de Gaulle of France warned Kennedy at the time that Vietnam was 'a bottomless military and political swamp.' It's a pity that Kennedy and his advisors chose to ignore the warning, a lot of lives could've been spared.