I don't have the lamp anymore, but i will do my best to explain the parts i have no picture of.
Step 1: Choose the Design and Pick Out the Wood
I used inventor to decide on the design. The overall dimensions is about 14" square by 6' 6" high. The mahogany posts are 3/4" milled into an L shape and the pine strips are 3/4" wide and about 1/32" thick. However, the dimensions are not critical and can be modified to fit however you want.
Step 2: Mill Wood
I used a jig as shown to rip the strips about 1/32" thick, and held them in front of the light to show how the light shines through them. The bottom foot of the legs were tapered with a hand plane.
Step 3: Assemble
The 3/4"x2 1/4" top pine frame was simple mitered, screwed, and glue together. And the posts were screwed into the frame from the top. Remember, there is very little stress on a lamp. The strips were glued with regular wood glue and and held in place for about 30sec each until the stayed on their own. It might be better to use a faster drying glue though. The lamps was scavenged from an old lamp, and the light was attached by making a piece of wood go glued diagonally in the middle of the lamp and screwing the light holder to the middle of it.