The main way was through schools established by various northern aid societies with and in some cases for the Freedmen’s Bureau (Bureau of Refugees, Freedmen, and Abandoned Lands).

In some cases, before the Freedmen’s Bureau came and became involved, missionaries from Northern States had already established Schools.

These schools focused largely on the basics, reading, writing, and math. In some places, school was offered during the day for younger people and in the evening for working freedmen.

The schools, some of which were taught by Quaker missionaries, offered Sunday School on Sunday.

Although the Bureau wasn’t involved in education in terms of a lot of direct funding or determining curriculum, it did in many cases build or rent the buildings for the schools, and provide military protection, and in some cases overall supervision of the schools.

There were a few instances where the freedmen actually had to put up or find the land for these schools. Columbus, Texas is one. A Freedman named Benjamin Franklin Williams had acquired several lots in the burgeoning Freedmantown community, and one of his was used.

The Bureau of Refugees, Freedmen was more heavily involved in education than some historians revealed in the early 20th Century. In fact pages and pages of correspondence and reports on schools and education exist in the Freedmen’s Bureau archives with the Library of Congress and National Archives, much of which has now been digitized. School matters, in fact take up an outsized portion of correspondence in some of the bureau regions.

After these schools closed (and they closed at different times; the bureau and missionaries pulled out of Georgia, for example, in 1870), the responsibility was upon the states.

In terms of older freed people, I would suspect a thorough review of the WPA Slave Narratives would provide one or two primary sources on the children who attended school teaching older relatives on occasion, but I cannot lay my hands on such a reference at this time.

Sources:

Butchart, Ronald E. “Freedmen's Education during Reconstruction,” New Georgia Encyclopedia.

Crouch, Barry A., The Freedmen's Bureau and Black Texans, University of Texas Press

Butchart, Ronald E. Schooling the Freed People: Teaching, Learning, and the Struggle for Black Freedom, 1861-1876, University of North Carolina Press