Short answers, pulled from the story.
The Bay of Pigs Invasion took place in April 1961. The main landing force entered the Bay of Pigs at midnight on the 17th of April 1961, and the invading force surrendered on the 20th of April 1961, three days later.
The Bay of Pigs Invasion was planned by the CIA and clandestinely financed by the U.S. government. Richard M. Bissell Jr. was charged with overseeing invasion plans, working under CIA Director Allen Dulles. President Eisenhower initially approved a CIA budget of $13,000,000 to explore options for removing Castro, and President Kennedy approved the final operation on the 4th of April 1961.
Brigade 2506 was led by Dr. Manuel Artime as the overall civilian leader and José "Pepe" Pérez San Román as the military commander. Artime had previously served in Cuba's revolutionary government before defecting and was recruited by CIA officer E. Howard Hunt.
The invasion failed for several interconnected reasons. President Kennedy canceled planned follow-up air strikes on Cuban airfields late on the 16th of April to preserve plausible deniability of U.S. involvement. The CIA itself had judged the original plan required U.S. air and naval forces; without them, the operation proceeded with fewer resources than planners said were necessary. Cuban security services also knew an attack was coming in advance, and the Cuban Air Force destroyed key supply ships, including the Houston, early in the battle.
The defeat pushed Cuba closer to the Soviet Union, directly setting the stage for the Cuban Missile Crisis in 1962. Castro's government victory solidified his standing as a national hero inside Cuba and widened the political division between Cuba and the United States. The failed invasion also emboldened other Latin American groups to undermine U.S. influence in the region.
Brigade 2506 received infantry training at a CIA-run base code-named JMTrax in the Helvetia coffee plantation on the Pacific coast of Guatemala. Tank training took place at Fort Knox, Kentucky, and Fort Benning, Georgia. Underwater demolition training was conducted at Belle Chasse near New Orleans, and amphibious landing training took place at Vieques Island, Puerto Rico.