It is normally a long, arduous process, but the 1866 congress had an advantage over most other eras. They had occupation armies controlling the Southern states, and therefore the Southern states would rubber stamp anything they were ordered to pass.
Using guns to force states to vote certain ways is not how the framers envisioned constitutional amendments, I think.
But that is how it was done.
The Constitution is silent on a state’s ability to secede so the Supreme Court essentially legislated from the bench in Texas v. White (1869) declaring secession illegal which avoided a Constitutional basis. So much for the sanctity of the Judicial Branch! So we are left with what Mao said, “ power comes from the end of a gun”.