Chris says:

"I used a small screwdriver right at the top of the clock, and that popped it right out. Wiggled it a bit, and the bottom also came out. 

Removed the 2 connectors - the plastic was a bit brittle on one, so be careful. 

There are 5 small screws holding the case together - remove these. You'll also need to pop off the "button" in the center of the clock. Pull it straight out. 

There are 2 screws holding the switch circuit board together - I removed these to check the voltage going to the lights, but you don't need to do this just to replace the bulbs. 

I found exactly the right bulbs at radio shack - part #272-1092C contains 2 12 v. 60mA wire-terminal base bulbs. The only difference is that the bulbs are clear (the stock bulbs are frosted).  Unsolder the old, and put in the new. You'll need a pretty small soldering iron to avoid melting the switch a bit. 

Re-assemble, and reinstall. 

Total time: about 30 minutes 
Total cost: under $2.00"