This is a matter of a great deal of debate. No one really knows for sure.
The most common answer today is that the freed slaves were very important in shaping life after the war. They are given credit for reestablishing family structure that had been hurt by slavery. They are given credit for starting black churches that would become a pillar of the black community.
They are not, however, usually portrayed as having had much to do with the government of the South during this time. This is a backlash against previous views of the subject that said that governments in the South were terrible because they were controlled by blacks who lacked the education and experience to be good legislators. Today, most historians see Reconstruction as a failure and they tend to lay the blame at the feet of whites, both Northern and Southern.
Some scholars, notably Thomas Holt (himself African American) argue that blacks did have a great deal of influence in government as well. Holt argues that black elites are to blame for the problems of other blacks because they looked down on the lower class blacks and did not do much to help them.
Overall: most historians give credit to blacks for shaping their own lives but do not blame them for the problems of Reconstruction. (You can see this approach in the first answer posted here.) Some revisionist scholars have started to argue that black elites, at least, deserve more blame than they get.
Following the Civil War The Emancipation Proclamation set an end to slavery. One of the most significant contributions by African Americans during the period was the aid they provided to help to educate former slaves. Many of the slaves had been denied the opportunity to read and write. Education was the key to enabling them to be able to better understand the white society and to begin to find a place among the hostile environments they entered.
For the first time in America, black men were given the right to hold political office although it was not without struggle. Many helped to shape political policies. Booker T. Washington helped to establish a school where former slaves could learn hire-able skills. Black families were able to shape their own family structure. Formerly they had been split apart due to slavery. They could now determine who to live with as family members.
Former slaves were under terrible pressure to join work gangs but their desire not to return to a pattern of work reminiscent to slavery led to changes politically and economically. Black Americans began to emerge with more funds and political ties.
The African American influence and their refusal to allow the South to fall back to previous patterns guided the resolutions of race which we have today and paved the way for the offices, education, and rights that all Americans share.