How did the South try to reinstate the social hierarchical status quo after the Civil War?

It's important to keep in mind, when answering this question, that Reconstruction proceeded in multiple stages, and the situation evolved as the conditions did. Nevertheless, across the entire time period in question, the South remained reactionary and continually resisted Reconstruction efforts to reform Southern society.
When looking at Reconstruction, it is important to differentiate between the years before and after 1867, when the Radical Republicans gained a majority in Congress and was then able to pass the First Reconstruction Act. This was the time period that saw passage of the Thirteenth Amendment, which banned slavery. However, Radical Republicans were ultimately disappointed in the overall tenor of Reconstruction in this period.
During this time period, the Southern States elected to Congress former Confederate politicians and leaders: this alone is a sharp signal that the South would try as much as possible to create a post-war settlement that restored the pre-Civil War status quo. In addition, Southern States passed the Black Codes to restrict the rights and opportunities of newly-freed slaves. Finally, you should be aware of the Freedmen's Bureau, which was created to provide education and support for former slaves and impoverished whites. However, the freedmen, alongside workers associated with the bureau, often faced harassment and poor treatment at the hands of the local wealthier white population.
As the Radical Republicans took over, the situation changed. Southern State Constitutions were suspended, and the South was split up into military zones under martial law. During this period of time, the Fourteenth Amendment (expanding citizenship) and the Fifteenth Amendment (granting voting rights) were passed. Here many Southern whites turned to violence and intimidation via groups like the Ku Klux Klan, while others turned towards more passive forms of resistance.
Ultimately, Northerners lost the will to continue Reconstruction, and it was officially closed in 1877. In the aftermath of this moment, Southern States passed Jim Crow laws, instituting systemic segregation between black and white people. Literacy tests and poll taxes were set up to prevent black people from exercising their voting rights.
Finally, I would suggest you look into the history of sharecropping and the ways in which black farmers ultimately remained under the domination of white landlords.