The design for the high voltage circuit was originally done by Tom Napier and published (I think) in Nuts&Volts. There might be a reference in his Circuit Cellar article referred to above.
Basically, you know how much energy can be stored in the inductance, from the current (1/2)Li^2. The maximum inductor current is controlled by the ~22 ohm resistor to ground, which triggers a transistor to switch off the 555 thus controlling the duty cycle.
Then you need to know what the current draw of the Geiger tube will be, assuming some maximum count rate. The average Geiger tube current*500 V gives you the power draw. The switching rate of the 555 is set to produce a bit more than that power draw (energy stored in inductor/time).