Basically, it's as simple as this: you apply 12 volts of electricity across the ingoing black and red leads, and out comes 2,000 volts "unknown frequency", (although I'd say it's pretty high because of the spark gap noise when it get's too wide), AC. This is enough to jump a "small" gap, (think in the spark plug range), but the gap can be drawn out after firing it up initially, because the air between electrodes has become ionized. I think some sort of mechanism like in a camera flash, to ionize the air between spark gaps before firing up, can provide a good method to get longer sparks as well.
These things are cheap. You might even be able to find them at a hardware store somewhere, (their used for setting up neon-tube sign displays).
And finally, here's some pictures.
<div align="center">The transformer... note simplicity...
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</div><div align="center">The spark gap. This is in a "drawn out" state, and emitting a high-frequency noise...</div>
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