I agree that it may be easier to start with a somewhat simpler
circuit to teach the basics, but understanding what the circuit
does is a good start to knowing how to simplify it.
First, always break the circuit into component blocks. In this
case, the transformer, rectifiers and filter caps, the pass transistors,
the regulator, the over voltage protection, and the metering.
The simplest power supply might just have a transformer,
rectifiers, and filter capacitors to generate DC. It's unregulated,
so the output voltage will vary with the load, but adequate for a
lot of less critical applications. There are several variants: this
uses full wave rectification with two diodes on either side of a
grounded center tap. (Each side of the secondary delivers
current when it is positive with respect to ground.) When the
winding doesn't have a center tap (or you need the full winding
voltage rather than half of it) then a full wave bridge with
4 diodes is used. For low current applications, a single diode
with half wave rectification may be good enough.
The pass transistors are what adjust the output voltage up
or down as needed, controlled by the regulator. They are
often separated from the regulator because the major
concern is heat dissipation at full current. In this case, there
are two transistors, with emitter resistors which help to
balance the current between the two transistors (an example
of something that isn't required with a single transistor,
but improves the long term reliability of the supply).
The regulator in this case is an LM723, a common integrated
circuit with lots of features. However, that makes it more
difficult to see exactly what it is doing without having a
data sheet handy. A simpler regulator might just be a
single zener diode.
The metering circuit includes a voltmeter and a current meter.
Rather than running the whole current through the latter, it
actually displays the voltage drop across one of the emitter
resistors, which simplifies the required meter movement.
The overvoltage protection circuit is buried in the regulator.
It consists of zener diode CR4 along with SCR1. When the
output voltage is high enough for CR4 to conduct, it triggers
the SCR, which short-circuits the output (like dropping a
crowbar across it, hence the name) until the regulator shuts
down or the fuse blows. That provides protection in case one
of the pass transistors shorts, which could otherwise damage
your radio.
There are lots of other parts that aren't necessary for a simple
supply, but are added for good performance. As G3RZP said,
the LM723 is prone to RF, so there are numerous bypass
capacitors added to reduce the problem. There are also
extra diodes to protect the supply from damage in case there
is voltage applied to the output when the AC power is switched
off (for example, if the supply is used to charge a battery).
But the first step is always to break it down into component
blocks, then it is easier to see how the blocks work together.
There are multiple circuits that could be used for each of the
blocks, depending on the requirements of the supply.