The geothermal (heat) energy is used in exactly the same way that thermal energy from burning fossil fuel, or neuclear energy, is used. The heat is used to change water into steam which turns a turbine, which then generates the electrical energy from a dynamo or alternator.
The only difference is that the geothermal energy is tapped deep in the ground and is non polluting, and long lasting as a renewable energy source. The heat energy is harvested by passing water into the geothermal heat source for conversion to steam. Another method uses naturally occuring boiling superheated water or steam directly from the ground.