In this post, I am only showing the base of the lightsaber. It's quite straightforward. I am using four super bright LEDs from Sparkfun, two 220 ohm resistors, a 9V battery, and a switch. For the housing, I cut down some PVC pipe and bought some fittings for the end. The most expensive piece of equipment is the switch at about $4. The entire lightsaber comes in under $10.
As an exercise, I had Devin (the 9 year old) use this website, which generates a circuit and the necessary resistors for a given number of LEDs. It's a good tool and perfect for a child with very little knowledge of Algebra. I'll include a schematic of the LED circuit below. I have also included pictures from throughout the project.
After I finished James' (the 5 year old's) light saber, Devin decided to solder his up tonight too. They both turned out rather well. All that is left is attaching the tube.