Electro-magnetic repulsion. Pump a current through a loop. Result, a magnetic field. Put one magnetic field in proximity with a second (the tethered system and the Earth's magnetic field). Depending on polarity you either get repulsion or attraction. The total thrust is very small, but since there is very little resistance, you still move away from the Earth or towards the Earth with every orbit.
Buck Rogers stuff that is for real. The only thing is ya gotta be patient.