This is the product I'm refrering to. I have seen this product being used in many DIY and wanted to know the circuit it uses and how it is able to step up the voltage so high in such a small space and price.
These circuits based on three stages first DC to high frequency AC using PWM chip and then connect a high frequency switching transformer.(the transformer turn ratio tell the high voltage).The transformer(ferrite or torride core) converter low voltage high frequency AC to high voltage high frequency AC. After this stage we connect the high frequency switching diode which convert AC to DC. The explained block diagram is shown below. The purpose of using high frequency switching transformer is to reduce size and increase power.
It contains an AC oscillator and a step up transformer. The AC oscillator converts the DC voltage to alternating current which the transformer then steps up to a high voltage.
Many people homebrew a similar device using an ignition coil from an older vehicle as the transformer. It will not develop as high of voltages as claimed in the ad (which are quite dubious) but it does make a simple source for high voltages. Use these terms to search the web for DIY instructions.