How did African Americans shape the course and consequences of the Civil War from 1861-1870?
African Americans helped to shape the course and consequences of the war during this time frame by helping to make the war and its aftermath be about them. The war was not necessarily going to be about African Americans, but African Americans helped make it that way. They were, of course, not alone in doing so.
At the beginning of the war, the war was only about preserving the Union. We know that Abraham Lincoln said that he would refrain from freeing any slaves if he felt that was the best way to preserve the Union. But then the war turned and came to focus more on African Americans. Perhaps the major factor to cause this change was the Emancipation Proclamation.
Although African Americans did not, of course, issue the Proclamation, their actions after that helped turn the war into a war about them. African Americans served in the Union Army in relatively large numbers on a volunteer basis. They did so even in the face of great prejudice and discrimination. After the war, African Americans pushed for the government to help them economically and socially. The freed slaves wanted the right to vote and the right to be treated equally and they wanted economic opportunities. Their desires, and the desire of many Southern whites to stop them, helped bring about Radical Reconstruction by 1870.
Because African Americans fought bravely in the war and because they pushed for greater rights in the time after the war, the war came to be seen as a war that was largely about African Americans, their freedom, and their status after being freed from slavery.