One major participant in Reconstruction was the federal government, which, under Radical Republicans, took measures that temporarily enfranchised freedmen, completely altering the political landscape in the South. Another group of participants were black men and women, who took advantage of the limited opportunities available to them and tried their best to carve out lives for themselves. Most entered into sharecropper or tenant arrangements, but many also started businesses, went to the host of new schools founded by the Freedmen's Bureau and private organizations, and attempted to reunite their families. Another major participant were southern elites, who used any means necessary, including violence, to wrest control of state and local governments from black and Republican control (as well as that of poor whites). Another participant in Reconstruction has been the legion of writers, film makers, and purveyors of popular culture that have perpetuated the "Lost Cause" myth of the Civil War and Reconstruction, with consequences that continue to reverberate through our politics today. There is an abundance of scholarship on this topic, with the work of Eric Foner, David Blight, Kate Masur, and Bruce Baker representing particularly important correctives to the highly racialized account of Reconstruction that casts the white South in the role of innocent victim crushed by a tyrannical North bent on instituting capitalism and "black rule."
The people of the South were directly affected by Reconstruction, because they had to live with it. They had been hit hard by the war, because it had happened on Southern soil. In the end, they had to buy-in to accomplish anything.
Ulysses S. Grant understood the exploitation of the South after the Civil War, a time mistakenly called Reconstruction. For the Northern shysters who came to be known as carpetbaggers were simply greedy opportunists, and Grant wanted them removed from the South. There was no legitimate effort to aid blacks to assimilate into the new social situation. Falsely told that they could have "Forty acres and a mule," the blacks were, in truth, exploited by many who came from the North. When the North burned a path from Atlanta to the sea, how could that government possibly be perceived as altruistic?
Had there been genuine concern for the disenfranchised blacks, efforts would have been made to make them literate and able to live independently. Instead, they were simply released into a world they did not know without any provisions for their assimilation.
Bottom line: The North crushed the South and left it that way. That total defeat and ruin was the clear purpose of the North was exemplified by Sherman's "March to the Sea" burning everything in its path.
This really depends on how you look at it.
I suppose that the major participants were Abraham Lincoln at first. After his death, there was Andrew Johnson. There were the Radical Republicans. Of course, during that time, white Southerners were also major actors. There were the "scalawags" who helped with Reconstruction, but there were also the white Southerners, like those in the KKK, who worked to thwart the goals of Reconstruction and to "redeem" the South. Another group that was important was African Americans in the South. They participated in the Reconstruction governments and their voting power made them important both as a source of Republican votes and as a target of the KKK.