Here are the raw materials.  This is the oak and plexiglass.

I decided to use the good old miter box to make sure the edges of the oak stayed straight.

Shown here is the initial stacking of material to see how things are lining up.  Starting to look like the final product!  I used a scoring tool to cut the plexiglass.  I made several passes until I was halfway through the material and then snapped it off.  Worked out pretty good but will need some trimming.  This is also where I drilled the one inch hole into each individual piece.  I do not have a drill press to I tried my best to center the holes by eye.  I used a cordless drill and a one inch bit to create the holes.  The plexiglass was more difficult to drill through than I thought.  To keep everything together I used two part clear epoxy.  After taking the clamps off I noticed that the pieces had all shifted slightly.  I figured I would trim this using an electric miter saw.

Here we see the piece after it has been trimmed using the miter saw.  I do not own one so I had to use my father-in-law's saw.  Everything went smoothly and I kept all of my fingers.  After the trimming was done I sanded off the few burn marks left by the miter saw.  I also sanded the corners off to give it a nicer look.

The LEDs arrived in the mail and I did a test fit to see what it would look like and also to see how many lights I would need to cut off.

These are the lights that I used.  I guess I forgot to take a photo of them before putting the bottom of the light on.  After a couple attempts at figuring out a good orientation, and trimming off the right amount of lights from the end of the strip, I coiled them up inside the one inch hole in the middle with the lights facing outward.  I decided to go with USB so that the light can be plugged into a computer.  Using an adapter, like what comes with most cell phones, the light can also be plugged into a standard wall outlet.

This is a look at the bottom of the light.  I drilled half of a hole from the outside edge to the inner hole to allow the cable from the lights to sit below the surface of the wood.  I have some brass screws holding the metal plate onto the bottom.  I thought the screws might make good feet but I ended up using some silicone feet to avoid any scratching.

This will give you a rough I idea of the amount of light put out.

Here is the finished product.  I used some dark oak finish on it as well.  I think it turned out really nice!