Generally that is done through a separate winding on the transformer, that gets rectified and filtered. This is called the bootstrap winding because it can only provide power after the P/S starts up.
Generally, a failrly large cap is used to store enough energy to get the circuit started until the boostrap winding can deliver the power.
The advantage is that the voltage to the circuit is semi-regulated and the efficieny is somewhat higher, since all those parts are powered from a voltage that is lower than the input voltage, so for the same current the power consumption is lower, even factoring in the P/S efficiency.
There are situations where you cannot have this winding (such as in non-isolated converters, where simple off-the-shelf inductors are used). In this case, if the input voltage range is acceptable, you power the parts directly from the input voltage.
There are other situations where you actually have an auxiliary converter (a P/S in itself) used only to provide power to the auxiliary circuitry. This is especially important when the main P/S has to have the ability to shut down.