[Warning and Disclaimer: This involves high voltage electricity and burning wood. Do so at your own risk. To reduce risk, educate yourself. I cannot be held responsible. Be safe!]
I wish I could take credit for this, but this link will take you to the artist who got me interested in this process. After scrolling through the comments and the comments of other YouTube videos, I figured the easiest way to get the voltage I needed was with a neon sign transformer. These transformers come in all shapes and sizes ranging from 2000 volts up to 15000 both a/c and d/c (but go with a/c). The type I use is 9000 volts and it is the old school, copper wrapped iron core transformer, not newer solid state transformers (which I understand will burn out quickly). Transformers are available on Ebay, but you might check with a local sign shop as they may have some available as well.
Once you have a transformer in hand, make sure the leads coming off it are long enough for the work intended. The one I received had only had about a foot of wire coming out the business end. I played it safe by adding a few more feet of insulated wire rated for high voltage but I suspect with such low amps, regular insulated wire would do. After adding the wire, I attached alligator clips to the ends and wrapped any exposed wire with electrical tape.
Now comes the fun part! I gathered up some small nails and a spray bottle full of salt water. I used sea salt for the latter. Prior to applying voltage, I wet the finished bowl with water to raise the grain, let it dry and sanded smooth. I then hammer in some small nails, usually 4 but sometimes more. I place them around the rim being careful not to pierce the bowl. (But that could be a fun experiment sometime…) I have discovered that the electricity tends to follow the grain. I place nails at the nearest to the pith and nearest to the bark. This works well for me, but feel free to experiment. I attach the alligator clips to two adjacent nails, spray with salt water and then flip the switch. Now watch the Lichtenberg figures emerge!