Step 1: Assembly
Remove the base of the lamp. There should be a rod inside that runs to the lightbulb. Remove this rod.
Next, place your Pi in a plastic case. Adhere the case to the lamp's rod. I used zip ties to secure it through the holes on the back of the case.
Plug in all necessary cords you need to run your Pi (power cord, ethernet, USB, etc). Run them into the lamp where the power cord would normally be found. I used a Dremel tool to cut an opening from the bottom of the lamp where the cords run through. I tried to prep the Pi for easy future modification without having to reopen the lamp by including an extra USB cable that could be used for a hub and wires coming off the GPIO pins.
(Side note - I recommend using an inexpensive lamp because you will likely need to make structural modifications. Inexpensive lamps will be made of plastic or other material that is easy to drill through. And, if you make a mistake and mar the lamp you do not get as upset).
One note, on the lamp I chose I found out that the I needed to use an SD card extender so that I did not have to completely disassemble the lamp every time I needed to access the SD card. You can now use one of the multi-boot distros built for the Raspberry PI so you can switch operating systems without accessing the SD card.