According to the Section 5 of the Congressional Reconstruction Acts of 1867, the people of those rebel states would form a constitution of government in conformity with the US Constitution, they would elect a convention of delegates.
Those delegates would be elected by male citizens of those states, that had more than 21 years old, of any race or color or previous condition. They needed to be resident in that state for more than a year, but they would not be able to vote if they participated in the rebellion for the secession or felony at common law.