Well, literally. Not much electronics involved. I found a smashed bicycle's headlight and salvaged the PCB with the LEDs, the switch, a capacitor, and a bare chip under some white resin. I didn't even bother finding out what the chip was for.
I did notice that the PCB would fit snugly in the outer shell of a 9V block battery, with the LEDs on the top on the side, and the switch on the back end. So I added a 7805 and put the PCB in the casing and connected the power leads to the former battery's contacts. Then, I filled the thing with a transparent pourable resin through the holes I drilled to let the light out.
How to connect power to it was rather obvious, and there it was; very portable, and battery change doesn't get much easier, as long as you make sure you don't throw away the LED bit by mistake and connect the old battery to the fresh one. This will generate heat, not light, and may explode one or both batteries.
The LEDs do pull quite a bit of current; lowering the voltage across the LEDs and using a switching regulator would help, but I couldn't be bothered as this is only a gimmick.
Why did I build this? Because I think it looks funny.