The idea behind this little experiment is that with volatile liquids, the gaseous fumes are what burn, not the liquid itself. As the name implies, the wickless lamp is a fire lamp which requires no wick to draw liquid fuel to be burned, for example, a candle.

There is a proper way to do this, with proper equipment and procedure. I did not choose this method, as I am of very modest means. I will only write about my haggard, bass-ackwards method as I am not completely sure of a proper procedure.

You will need:

First, light the candle. Wait until there is some melted wax near the wick. Dip one end of the pipette into the liquid wax and alow the plug to harden. Once the plug has hardened, use the syringe to fill the pipette with alcohol, leaving approximately one centimeter empty at the top. Place the pipette over the flame at the point where the "alcohol line" is. Wait a few seconds, you are heating up some alcohol to produce vapor. Pass the open tip of the pipette near the flame to ignite the vapor. If it does not ignite, heat it up a little longer. If the tip has a flame coming from it, immediately move the pipette so that you are again heating up the "alcohol line" to produce more vapor to feed to the flame. You should have a consistent orange/yellow flame with a blue base. If the vapor shoots out fast enough, the flame will hover out from the tip of the pipette and appear to float in midair. Keep slowly advancing down the pipette, following the alcohol line.
NOTE: There is a strong possibility that the flame may back up into the pipette and cause a sharp pop, shooting a droplet or two of boiling alcohol out of the end and either extinguishing or causing your flame to flare up. Don't panic and don't point it at your face or anyone else's. Ever.