That process was called VIETNAMIZATION.
President Nixon was the one who instituted the Vietnamization policy, which emphasized that the United States must empower South Vietnamese forces to assume more combat duties.
By the time the US was shifting emphasis to this sort of policy, it was too late to stave off the victory of the North Vietnamese and Viet Cong forces. The US eventually withdrew its forces from Vietnam in 1973, and by 1975, Saigon (in South Vietnam) fell to the North Vietnamese communist forces.
