There are two methods to making a plasma globe. Both use AC flyback transformers, but they use different drivers. This is important to know because you will be building the driver yourself and you want to choose your method based on a few different factors.
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.