Graphite is commonly used to make electrodes for sinker EDM, and complex shapes can easily be machined on the electrode.
The process itself involves connecting a capacitor between a positively charged workpiece, and a negatively charged electrode. The capacitor provides very short bursts of high current, at the point where the dielectric fluid separating the work and electrode is so thin that an electrical breakdown occurrs. It this point, a spark is created, dissipating the energy stored in the capacitor, and vaporizing a tiny bit of workpiece material. Due to the polarity of the current, much more energy is depositied in the workpiece material than the electrode, thereby preserving the shape and size of the electrode.
The dielectric fluid concentrates the discharge, carries away heat and workpiece particles, and keeps oxygen away from the work area. Light oils like kerosene make ideal EDM fluids, but the risk of fire is substantial. Therefore, less flammable fluids should be used. Tap water has too many ions to be useful, as electrolysis produces a lot of foaming and Hydrogen and Oxygen, which are another danger.
For best results a feed mechanism controlled by the EDM current is desired. It even needs to back up if the electrode shorts out to the work. The feed needs to be very fine, in steps of no more than .0001", and finer if possible.
A method of flowing the EDM fluid through the electrode is desirable, to flush particles away from the area between the work and electrode. I have burned out broken taps with just a wire, with no flushing of the fluid. It requires you to pull the electrode back and clear out the dirty fluid every .010" of depth or so. But, for a quick and dirty setup for burning out a couple of taps, it is just the thing.
I used a voltage of about 30 Volts, at a current between 1/4 and 1/2 Amp.