A Slayer Exciter is essentially a transformer that steps up the primary voltage from the driver circuit (in this case, a high frequency oscillator) and creates a varying electric field that can light up fluorescent light bulbs. I found instructions on an Instructables article here.
The article calls for a pipe about 1″ in diameter, but all I could find was a 1.5″ pipe, so having about 400 turns on the secondary called for about 150′ of 30 AWG magnet wire. I winded the primary about 8 times, but found that it actually took 6 turns for the exciter to work. Since I decided to supply the circuit with 18 V, I attached a heat sink onto the TIP31C transistor.
If you do plan on making one of these, exercise caution since there are high voltages involved in the secondary winding.