These Hi-Lo switches have a diode in them to cut the alternating-current sine wave in half, thus halving the output of any incandescent lamp.

Flourescents, even dimmable flourescents, will only turn on and off.

To install:

With a narrow-tipped screwdriver, unscrew the two tiny machine screws that hold the case together, working over a clean surface so you don't loose the...
...two little nuts that will fall out their little hexagonal wells at the back of the case. Open the switch.

With a pair of diagonal wire cutters, cut half way across the cord, cutting the smooth side of the cord. The other side has fine ridges running lengthwise - look close!
Then cut up the middle of the cord about half an inch,
remove that half inch of the smooth side of the cord...
the cord is ready to install in the open switch half...
And here the cord is installed in the switch - a natural fit!
Squeeze the two sides of the switch together, fit the tiny nuts into their wells and drive the screws just tight enough to bring the sides together
...and use! If you install in the orientation shown - with the lamp in the direction of the top of the images, the knurled disc will roll in a downward direction to dim the lamp.