In the simplest case emitter follower is used, the base of the regulating transistor is directly connected to the voltage reference:
The stabilizer uses the power source, having voltage Uin that may vary over time. It delivers the relatively constant voltage Uout. The output load RL can also vary over time. For such a device to work properly, the input voltage must be larger than the output voltage and Voltage drop must not exceed the limits of the transistor used.
The output voltage of the stabilizer is equal to UZ - UBE where UBE is about 0.7 V and depends on the load current. If the output voltage drops below that limit, this increases the voltage difference between the base and emitter (Ube), opening the transistor and delivering more current. Delivering more current through the same output resistor RL increases the voltage again. When the output voltage increases, due to the reduced base-emitter voltage the BJT will conduct less and the regulation will be maintained.