This project will require a handful of parts, pictured below. Your project may vary slightly depending on the bulb you are replacing, but the basic idea will be the same. The main components are the LED and the driver.
The driver is a cheap 120VAC to constant current unit built and sold direct from China. This is not a particularly safe, elegant, or reliable driver but the price is hard to beat. When working with electricity, especially 120VAC, be careful and do not take any chances.
The LED is a Cree XRE high efficiency warm white source, rated at 74 Lumens at 350mA.
List of Parts
Cree XRE Warm White LED http://ledsupply.com/creexre-ww.php
(You should get the XPG now, since it is more efficient and cheaper http://www.ledsupply.com/creexpg-ww105.php )
3W 120VAC LED Driver http://www.dx.com/s/13552
Bulb to be replaced
Scrap of thin wood (plywood or popsicle stick)
Small section of aluminum channel for heatsink
Misc epoxy (i.e. JB Weld)