Answer: African-americans' rights were restricted and denied through no access to land of their own, the Black Codes, and several limitations on conceded rights like the right to education and the right to vote.
During Reconstruction the U.S. now had to integrate as rightful citizens a mass of people brought against their force, or born slaves, and former victims of immense violence, besides having to deal with unhappy white Southern elites.
The process of African-americans fighting and winning fundamental rights is still in process. During Reconstruction the resistence against African-americans' rights was explicit and violent. In 1866 the Ku Klux Klan was founded. It intimidated and killed African-americans so them didn't try to win their rights.
The sharecropper system left African-americans in a quasi serfdom status. They would work in a white man's land, using his tools, and give him between a third and a half of their production -- and it was the owner of the land who dictated the price.
The rights to education and to vote were sistematically attacked through segregation and/or overt obstruction by white supremacists.
There were also the Black Codes: groups of laws passed in Southern states to virtually keep African-americans as slaves. The most famous Black Codes are the ones passed in 1865 and 1866 which had the same text as the Slave Codes, only switching "slave" for references to African-americans.