The establishment of Jim Crow laws would be one way in which White supremacy was a part of post- Civil War Life in the South. These laws severely limited the political and social integration of African- Americans in the South. They helped to keep African- Americans locked in a condition that resembled enslavement, but was more insidious and more sinister in that it was legally enshrined and protected by the law. While slavery was something that could be physically identified and seen as representing supremacy, the use of the codified legal structure to help advance White supremacy at the cost of Black dignity was something more subterranean. At the same time, I would say that the social condition of African- Americans after the Civil War helped to keep Whites at the top of the social order at the cost of African- Americans. Few attempts were made to effectively integrate the lives of former slaves into American society. It was almost as if the war was fought, slavery was abolished, and that was it. For those who lived for generations of slaves, to be simply "thrown into" society without much in way of legitimate and effective transition programs and initiatives was a way for White supremacy to still be intact in the South even after slavery was abolished.
Two ways that white supremacy was restored in the South after the Civil War were through governmental action and through terrorism.
The terrorism was conducted by groups like the Ku Klux Klan. This group was created to try to frighten freed blacks and the white supporters of Reconstruction governments. The KKK used violence to try to prevent these groups from exercising their political rights.
Partly because of this, and partly because of Northern indifference, the Compromise of 1877 was reached. This compromise ended Reconstruction and allowed the South to have self-government again. Governments elected after this were uniformly white supremacist, taking away the rights of black people to vote and to have equal treatment.