Step 1: Making the parts

Picture of making the parts
 You'll need:

a small amount of wood: a 2 x 4 will be more than enough. I used less than half a square foot of 3/4 inch thick plywood. Cut and notch it as pictured, and you've got your basics done!

a couple rubber bands. The nice part about all this is that you can adjust the tension of your lamp by just adding another rubber band. You can also easily replace them--unlike the springs and pieces in your usual desk lamp

a light bulb and electrical socket

a sheet of printer paper

Cut the wood pieces--on a bandsaw if you're lazy, and by hand if you're really hardcore about it. Wood piece 4 is a small piece that slots into wood piece 3 after everything's done to constrain the range of motion of the lamp