I know there are a few others out there, but here is my tutorial for Sharpie dyeing a wig! This works best with Kanekalon and other premium synthetic wigs. Eleora and cheaper synthetic wigs may not dye evenly. Make sure to check your wig fiber content before attempting to dye!
I've had a lot of practice with this method, and this is the formula that works best for me, so I hope it can help you dye your wig the custom color you are looking for!
Many thanks to my friend Envel who helped me with my first Sharpie dyeing experience. Tutorial and all images therein are Copyright Fire Lily and FireLilyCosplay.com.EDIT: Since so many people ask this question, I'm addressing it here. "How do I dye a wig black?" Since Black Sharpies are concentrated purple, you will have to use FW Ink, India Ink, or another Artists Ink and follow the FW Ink Dyeing Method: [link]
Another method is to color/sharpie the wig by hand using a black Sharpie. This will give it a slightly purple sheen, but it will come out black.