Build the circuit.
Easy as pie. Battery + Power + Slide dimmer + Fan. Mount everything except the fan itself on a mounting board.
Add the arrow indicator
Create an arrow in the center of the fan using stickers. It should point to any of the four flat sides of the fan.
Prepare your display.
Take a plate or any other flat-ish object to serve as your display. Lay the fan flat on it with the cables facing down. Stick or write an "N" for north above the fan, an "E" for east to its right, an "S" for south below and an "W" for west to its left.
Use your "Compass of Fortune"
Turn the fan on with the slide dimmer. After letting it rotate for some seconds turn it off again. The dial will show in which direction your next day trip will go.