Speaking in terms of a small tesla coil, I built one using a kit I got at maker Faire. In Retrospect you really dont need a kit, but I did get a nice silver globe thingy!
https://www.teslatronix.com/
Ive set it up, used it, played with it, and now it just sits there. It was pretty cool to experiment with. I "tuned" it using my scope as antenna. I wound my coil using a lathe and going verrry slowly. I only got a few mm worth of sparks, but it lit up bulbs from 1-2 feet away. It seems they dont publish the schematic anymore, but it really isnt difficult to make, Its a "joule" thief of sorts but on a bigger scale.
ADD: More experimentation is required though. Since the schematic is simple, I wondered what would happen if I used a bigger transistor/Powersupply and more turns.
Schematic is shown in this video
Mine didnt have the two diodes.