How were the civil war amendments enforced in the decades after they were past?

After the Civil War a period called the Reconstruction began. The goal of this period was among others enabling the African-American citizens their hard-won civil rights and getting the rebellious states back to the Union. To enforce the amendments and to ensure that the new elections could be done and in which African-Americans would also vote, the US government put the former Confederate states under the rule of the US Army. It also temporarily denied vote to the former Confederate officials and forbade them to run in the elections.