What was the process of bringing the Confederate States back into union?

The process of bringing the Confederate States back into the Union was called Reconstruction.

Explanation:

Reconstruction refers to the time after the Civil War. The term indicates both that large parts of the country had to be rebuilt, and that the Southern states had to be transformed from slave economies to states where the former slaves were now free citizens with civil rights. So-called radical Republicans wanted to enact laws, institutions and governing powers that guaranteed such rights for all Americans, while Presidents Abraham Lincoln and Andrew Johnson leaned toward a more moderate line to try to stabilize the Union as quickly as possible.

During this time, the Constitution made three changes, known as Reconstruction Amendments. These abolished slavery and forced labor, gave equal protection under law, and prohibited discrimination on grounds of race, color, or past condition of slavery. Congress also passed the first Civil Rights Act, the Civil Rights Act of 1875, which banned discrimination in public transportation, public places and in juries. But after about a decade of rapid change, conservative forces struck back many of them, and the reconstruction period is said to continue even in 1877, when the last federal troops were withdrawn from the Southern states.

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Explanation:

In early December 1863, the president began the process of reunification by unveiling a three-part proposal known as the ten percent plan that outlined how the states would return. The ten percent plan gave a general pardon to all Southerners except high-ranking Confederate government and military leaders; required 10 percent of the 1860 voting population in the former rebel states to take a binding oath of future allegiance to the United States and the emancipation of slaves; and declared that once those voters took those oaths, the restored Confederate states would draft new state constitutions.