How was the American Reconstruction Period considered a success?
Overall it was considered a failure, but that didn't mean there weren't parts of it that were successful.
For one thing, the Reconstruction Era from 1865-1877 successfully amended the Constitution not once, but three times. Slavery was permanently and formally ended, freed slaves were given citizenship and black males over 21 the right to vote. This could never be legally taken away, although it was delayed and discouraged for a long time.
The Freedman's Bureau constructed schools for freed slaves and send 1500 volunteer teachers into the South to run them. Over the course of six and a half years, the Freedman's Bureau taught over 200,000 freed slaves to basic literacy. While most were still left untaught, that is a staggering number to be accomplished in such a short time.
Lastly, they did come up with a way to legally get the southern states back in the Union, and in a way they would agree to, when they adopted Lincoln's 10% Plan. This made it very easy for them to reapply for statehood and to send Senators and Representatives to Congress once again.