First of all, we must recognize that not all of the African Americans who had been slaves reacted in the same way after the Civil War made them free. Different individuals reacted in different ways, and there were even some former slaves who stayed with their former owners. However, for the most part, the ex-slaves exerted their freedom by doing the things that they had not been able to do under slavery.
One thing that many ex-slaves did was to exercise their right to work for themselves. The freedmen tended to try to do whatever they could to have economic autonomy. They tried to get land to farm for themselves. Those who had trades tried to set up in business. They tried to avoid being dominated by other people economically.
A second thing that the freed slaves did was to claim their religious freedom. In slavery, black religious rights had been severely curtailed because whites were afraid that black church services would be used as ways for slaves to meet and plan escapes or rebellions. The whites also wanted churches to convey the “right” message about slavery. When the African Americans became free, they created their own churches that would be free from white control.
Perhaps the most important thing that the ex-slaves did was to create their own official families. Under slavery, black families had no standing and no rights. Slave marriages were not officially recognized under the law. Slaveowners could and did break up families by selling wives, husbands, and children when it was economically advantageous for them to do so. After emancipation, African Americans wanted to have families that could be stable and secure. Many of them tried to find loved ones from whom they had been separated. They rebuilt their families and tried to make sure that they would be able to live together as families should.
In all of these ways, the freed slaves tried to exert their new-found freedom after the Civil War.