If the relay is clicking, it's probably working. I don't suppose you have a multimeter?
The AC side of the relay is probably wired incorrectly. In fact, the schematic on the instructables website doesn't show any AC power applied... It just shows a the relay contacts connected to an AC socket with no power. The current needs to flow through
the relay contacts just like regular-old light switch.
If everything is wired correctly, and you disconect the 2 wires going to the relay, and then connect those two wires together, the light should go on. (Turn the power off before messing with the AC wiring.