It uses very common building blocks. The high voltage power supply is a classical oscillator circuit used in many places where a low current and high voltage is needed.
TR is a step-up transformer salvaged from a xenon light circuit. You can find similar transformers in fluorescent tube portable flashlights and similar devices using battery operated fluorescent tubes..
T is a common NPN transistor. Many transistors will work in this circuit. I used a 2SD1207 just because I found it in my junk box. Test some different transistors. Ones seems to work better that others in this kind of oscillators.
D is a fast switching high voltage diode. I used a RG1M fast switching diode from an old TV set. Don't use 1N4007, it works fine at 50/60 - 100/120 Hz but fails at several kHz.
This simple high voltage power supply is stable enough if input voltage is stable, so I placed a 78L33 regulator in front of it. This limits the minimum Geiger's supply voltage to around 5 volts. The output voltage can be adjusted with the aid of the 22k variable resistor from about 200 up to 800 volts.
The tube used is a ZP1401 from Mullard, almost identical to the LND 712 useful to detect alphas, betas and gammas. RSense and RLoad are taken from the LND 712 datasheet (1 and 10 Mohms) in the same way as the operating voltage (500 volts).
The circuit was mounted into an aluminum box with a hole to get alpha particles to get into the tube mica window. To protect this extremely delicate mica window a wire mess cut from a desktop pencil bucket was used with great success.
I use regularly this geiger counter with a cheap RS232-USB adapter and works fine. I installed a switch to disable the beeper, very useful during long background monitoring periods.The whole geiger in operation draws only 30 mA so it can be powered from the USB port if desired.