Step one is to take apart and dissemble the hair dryer so just the outside shell of the hair dryer is left.
Step 1: Aruino Light
To get a light inside of the container use a led light switch setup with the arduino. Use one of the switches on the hair dryer already in place of the momentary switch.
Step 2: Fitting It All Together
Put the arduino in the back compartment of the hairdryer and use part of the hiding compartment to fit the breadboard inside. Wire the power supply into the handle and out the bottom to make the hairdryer seem functional and to power the arduino.
Step 3: Hiding Your Things!
Once you fit your arduino inside and screw it all back together you can use the compartment in the front to hide things like money or jewelry. Plug it in to use the light on the inside of the compartment so you can see inside better.