A while ago I bought a couple rolls of LED strips for my car and couldn't think of what to do with the leftover until I finally decided to stop paying $5.00 at a time for bulbs in my lamp that burn out every 2 weeks.
Its a fairly even conversion, and it turned out pretty well.
Step 1: Planning
I already had some LED strips, but if you don't have any LED's you can get a 16' strip on amazon for very cheap.
Check out your lamp and decide how and where you want to run the wiring for your LED Strips. I decided to use the original wiring and just tie a DC 12v adapter into it. (The reason for the 12v DC is because the strip I bought was set up to run in my car on 12v. Most LED's Run on 1.5V - 3V)
Step 2: Mounting the LED's
Decide how you want to mount the LED's, I had a nice plate in my lamp that made it pretty easy to mount.
On the LED strip that i have you can cut it about every 1.5", make sure that you cut it where it is supposed to be cut otherwise you can't tie two strips together.
Step 3: Try It Out
Now you can power it on and make sure all your LED's work. Mine turned out pretty bright for the number of LED's I used.