The circuit schematic could hardly be simpler --- I am fairly embarrassed that the best I could do to obtain it for insertion here was "Print Screen" in KiCad. All of the action is provided by an LM317 linear regulator which costs peanuts these days. The output voltage is given by:
Vout = Vref * (1 + RV1 / R1), Vref = 1.25v
Note that this is independent of the input voltage, although obviously it can't be greater. Also we want to choose R1 so that the output is at sensible values for differing positions of the (linear) potentiometer RV1. Given a transformer rated at 19v, we choose R1 = 680R, giving values of Vout:
RV1 Vout0 1.252k5 5.85k 10.47k5 1510k 19.6
Obviously the last value is a little too high, however this value of R1 gives the greatest precision for the transformer at hand.
The design is completed with a cheap LED voltmeter as shown below.
Simple extensions to this design would be to use a combined Voltmeter/Ammeter display (also costing peanuts); adding a current-limiting circuit, or a switched constant-current source, also supported by the LM317. Next time!