How exactly does Morpheus crew free Neo from the powerplant?
It’s never explicitly stated, but it appears in waking Neo up, they are able to convince the machine’s system that he is garbage. After he breaks out of the cell he is in, a component of the system removes the cable from the back of his head, and his cell is flushed into the waste disposal system. This leads to the sewers, which is where the Nebuchadnezzar is waiting. They pluck Neo from the waste and hoist him to their ship.