First, I cut the CD tower into 3 equal parts, the wooden part with jigsaw, and the metal column using a flex. I kept the metal column slightly shorter then the wooden part. Then I drilled holes in the columns to attach the wooden part.
Inside of the wooden part I glued a crepe paper, which has a nice texture and just the right transparency to create a nice ambient light. You could also experiment with different paper colors.
Using a fast glue I attached a bulb to the metal column with a short cut of the column in between, so that the bulb was situated in the center of the lamp, connected the cable and put all parts together.