The rudder consists of a pair of slightly conical (usually but not always - designs vary), semi-cones mounted on a pivot either side of the propeller with the long axis of the cone running fore and aft when the helm is midships.  They are pivoted about a vertical axis such that the cone may close off the propeller thrust aft of the propeller, directing the thrust forwards and thus creating motion astern.
In addition to the "jaws" of the cone being controlled the direction of thrust is also controlled by rudder direction. In this way, it is unlike the azimuth thrusters used on many medium and large vessels, or the outboard motors or stern drives used by some small boats, since these all use the directed thrust to avoid the need of a rudder altogether.
Modern equivalent include certain types of pump jets or Kort nozzle.
While not strictly Kitchen rudder technology, the "bucket" on some aircraft jet engines is an aeronautical derivative of the device.  When the deflectors are deployed, directing thrust forwards, they are equivalent to the Kitchen rudder in the "full astern" position.