They are simple in theory, but require a lot of safety measures.
Most people use a HV transformer from a microwave oven, powered through a Variac, and the HV powers the electrodes. Both electrodes must be gold, and you need a good mechanical device which holds the electrodes the correct distance apart, allows for adjustments, and protects you from the high voltage. It is lethal.
I think forum member Sven has a HV setup. He has a demonstration video on youtube I think. You might contact him.