The first was that states had to create new governments that were loyal to the union and that respected federal authority. Each state had to have a new government without old politicians in it and they would have to swear loyalty officially and that they would abandon old practices and would respect federal government's authority.
The second was slavery had to be abolished once and for all. This didn't only apply to southern states but to all states in general since for example Texas still had slavery after the war because it wasn't a secessionist country so the emancipation proclamation did not apply to them. They abolished slavery in their own local government and not by having it imposed on them. This was achieved by the thirteenth amendment.
