The Fall of Saigon was the capture of Saigon, the capital of South Vietnam, by the People’s Army of Vietnam and the National Liberation Front of South Vietnam (also known as the Việt Cộng) on April 30, 1975. The event marked the end of the Vietnam War and the start of a transition period leading to the formal reunification of Vietnam into a socialist republic, governed by the Communist Party of Vietnam.
North Vietnamese forces, under the command of the General Văn Tiến Dũng, began their final attack on Saigon, with South Vietnamese forces commanded by General Nguyễn Văn Toàn, on April 29, suffering heavy artillery bombardment. This bombardment at the Tân Sơn Nhứt Airport killed the last two American servicemen to die in Vietnam, Charles McMahon and Darwin Judge. By the afternoon of the next day, North Vietnamese troops had occupied the important points of the city and raised their flag over the South Vietnamese presidential palace. The South Vietnamese government capitulated shortly afterward. The city was renamed Hồ Chí Minh City, after the Democratic Republic's President Hồ Chí Minh.
The fall of the city was preceded by the evacuation of almost all the American civilian and military personnel in Saigon, along with tens of thousands of South Vietnamese civilians associated with the southern regime. The evacuation culminated in Operation Frequent Wind, the largest helicopter evacuation in history. In addition to the flight of refugees, the end of the war and institution of new rules by the communists contributed to a decline in the city’s population.
http://en.wikipedia.org/wiki/Fall_of_Saigon
BTW, that is not the US embassy as usually reported.
Nixon had promised in President Thieu in January 1973 the US would react if N Vietnam mounted a serious threat after the peace was sighed in Paris. The US had ended all military action in March of 1973. Nixon resigned in August 1974. N Vietnam, who was basically afraid of what Nixon might do, now felt the fear was eliminated and subsequently began a major invasion of S Vietnam ultimately resulting in the fall of Siagon.