I have experience working on my Geiger counter with GM tube. In general you'll obtain a transformer, find out what voltage you get from it, then attach the correct amount of Villard (diode-capacitor) stages until you reach a voltage sufficient to trigger your GM tube.
That type of voltage multiplier can also be constructed with two symmetrical sections when it is known by the name Cockcroft-Walton. It's popular because no component must endure more than the incoming supply voltage. (Thus if you have 120 VAC, each diode can be rated 200V, and each capacitor can be rated 200V.)
I built a similar voltage multiplier in order to step up house voltage 120VAC to about 900 VDC. It required several diode-capacitor stages. The caps were 500 pF but this value was insufficient and I ended up joining a second cap in parallel to each. Eventually I was able to test my GM tubes. A click showed up on my oscilloscope. As a precaution I installed one or more 1 Mohm resistors.
The tube needs a minimum voltage so that it starts to detect normally. It can tolerate a higher voltage and presumably increase sensitivity however if you apply too great voltage it shortens its useful lifetime.