Before we make this project, I have to warn you of the safety issues.
This device outputs high voltages as much as 25,000 volts and can kill you. DO NOT SUBSTITUTE ANY PART OR PARTS FOR COMPONENTS OF DIFFERENT VALUES! It is crucial for your safety. I would recommend you do some research on high voltages before attempting this project. Also keep in mind that this is not a beginner level project and you will need to have experience in working with flyback transformers, high voltages, and lethal currents.
You have been warned.
Step 1: The Methods: 1 and 2
Method 1 uses a 555 timer to switch on and off a mosfet. It uses less components and is easier to build.
Method 2 uses a TL494 chip that can be bought online. This one is more complicated, but it gives you more control over the circuit and even lets you input audio.
I recommend method 1 for beginners because it is easier to get the desired frequency that you want. The frequency is also set to a safe value assuming you use the correct components. This is important because if the frequency is too low, then you will get a nasty shock. At the end of this instructable, I will show 2 videos that tell you how to tune the driver so that the arcs are safe to handle.