The conflict in Vietnam was between Ho Chi Minh and his Viet Cong and the French until the French withdrew in 1954 following their defeat at Dien Bien Phu. At the time Eisenhower had been in negotiations with the French and he and his cabinet considered the options for the conflict but were unwilling to get involved without participation from other nations, in this case the British. Without their commitment, Ike decided that getting involved wasn't worth the political cost.
Kennedy was more willing to buy into the domino theory and considered it a danger that Laos and Cambodia would fall to communist rebels if South Vietnam were allowed to go that direction. He was warned that they had almost no understanding of Vietnam, its history or its culture and that this lack of understanding would lead to serious problems but he continued to pledge support of Diem's regime.
Kennedy and then Johnson continued to build up US forces in South Vietnam, starting with advisors and then basically slowly allowing them to play more of an active role until Johnson used trumped up conflicts between naval vessels to justify sending in combat troops and significantly escalating US involvement.