Well, to look at how the South "won" Reconstruction, you have to look on the day after April 14th. Andrew Johnson, the war Democrat, takes office due to Lincoln being assassinated by Booth.
Andrew Johnson was the only Democrat from a Confederate state that remained loyal to the Union, and was picked as a running mate on the 1864 Election to send a message of national unity. The grand irony of this would be that Andrew Johnson, a southern, white supremacist, would be in charge of Reconstruction.
The Union Government had two plans in mind for reconstruction: Lincoln's 10% Plan and the Wade-Davis bill, passed by Radical Republicans within Congress.
Lincoln's 10% plan called for at least 10% of a Southern state to take the Ironclad oath, which would then allow it to rejoin the Union. He would also issue a blanket pardon to all Confederate figures. Lincoln firmly believed that a lenient approach was important in keeping the Union together.
Radical Republicans on the other hand, preferred their own Wade-Davis bill, which called for a Southern state to have 50% + 1 of its voters to take the Ironclad Oath. The Wade-Davis bill called for the trials of the Confederate leaders. This was rejected by Lincoln because he believed it would only harm the reunion of the United States.
Now, Lincoln's plan was never executed for the fact that Lincoln was killed before he could ever execute it. Andrew Johnson takes the presidency and has his own plan. Johnson's plan called for provisional governors and the passage of the 13th Amendment. Johnson's plan also issued a blanket pardon to all Southerners, with the exception of the aristocratic planter class, who had to appeal personally to him to be pardoned.
Johnson's vague statement allowed for the former Confederate states to pass the 13th Amendment, but it did not offer equal rights to freed slaves. This allowed for southern states to passed black codes which severely limited black rights.
Now this is where the North starts losing. Johnson was constantly at odds with the Radical Republicans. Radical Republicans passed the Civil Rights Act and an extension of the Freedman's Bureau, but it was pocket vetoed by Johnson. This veto was overruled by the Congress and passed without presidential approval. Congress would then pass the 14th Amendment, also fought against by Johnson, to protect the newfound rights for blacks.
A year later, in 1867, Congress passed their own version of Reconstruction, featuring the following:
Johnson, unsurprisingly, fought against this too. The partisan politics of Johnson vs. the Radical Republicans prevented an adequate solution due to constant bickering and disagreement. The Radical Republicans would not have to deal with President Johnson after he could not secure party nomination.
The Civil War ravaged the Southern landscape. With a few exceptions, must of the preexisting infrastructure has been destroyed to some ruin or extent. Obviously, the Civil War had ended the slavery system. Yet, where would these slaves go? Most of these slaves have been agricultural labors all their life, and it is the only thing they know how to do. The planter-aristocracy class needed laborers. So in exchange for supplies, shelter, and equipment, former slaves and poor whites would work a planter's land for a portion of their crop harvest. Planter's kept exorbitant credit rates, effectively keeping these laborers tied to the land. This was known as sharecropping. Sharecropping would lead to the South's return to a deeply agricultural lifestyle, as it was antebellum.
The Radical Reconstruction Plan allowed for US troops to enforce black liberties. This effect allowed for a coalition to form in support of the Radical Republicans. Scalawags (southern sympathizers of Reconstruction), Carpetbaggers (Northern Republicans moving into the South to rebuild), and freedmen. The presence of the USAA allowed for the election of some blacks into political office for a short duration.
The Radical Reconstruction plan allowed for 8 former Confederate states to rejoin the Union in 1868, just in time for the Presidential Election. Thanks to a bloody shirt being waved and the black vote, Ulysses S. Grant was elected.
Terror groups such as the KKK would suppress the black vote through terror and intimidation, however. One of the greatest examples of this would be the Mississippi Plan. Even with the Force Act and KKK Acts being passed, Grant could not consistently enforce these Acts and the KKK successfully limited black voting to a degree. This effect would be noticeable in the 1876 Election, where only three states in the South remained Republican, compared to the 1872 Election where 6 were Republican.
Southern elites also called for a return to the antebellum rule of whites. Such people were called redeemers, seeking to redeem Southern society. Democrats actively backed the KKK and some were Redeemers.
The military occupation of the South was costly, and the Panic of 1873 sent the US Economy in a downturn. Northerners began questioning the role US Troops. Support for Reconstruction declines in the North is beginning.
The Election of 1876 is traditionally seen as the death knell for Reconstruction. Skipping over the election itself, the Compromise of 1877 effectively kills Reconstruction. By handing over the election to Hayes, Republicans promised to withdraw Federal troops from the South. This left blacks unprotected, and black voter suppression became the norm. This ended Reconstruction, leaving blacks to the mercy of Jim Crow Laws for almost another century.
Source: Enduring Vision, Chapter 16