Here's my quick and dirty (and cheap) project to replace the lamp on my old laptop, who's backlight burnt out recently. I expect you could make this look a lot better if you were willing to put some more money into sourcing parts.
Materials: Screwdrivers, Dremel, electrical tape, wire crimping tubes.
The specifics of disassembling any particular laptop are going to vary widely, so I'm going to skip that step for simplicity. If you're not confident just diving in to your laptop, you'll frequently be able to find illustrated parts breakdows (IPBs) at the manufacturer's site for some guidance.
NOTE: High resolution photos available on Flickr: http://flickr.com/photos/killerrobotclan/sets/72157605872353185/detail/
Step 1: Getting at the lamp
I bought a generic white CCFL tube at a locally owned hobby shop; these are also available online. The easiest way to test that the laptop's inverter would light it correctly was to hook it up. I used simple wire crimps to splice the wiring tail from the old lamp onto the new one, and plugged everything in. Looks good so far.
Step 2: Electrical tape, Part 1
Sine the diameter of my replacement lamp is too big, it won't fit into the original mounting assembly, so I'm securing it with electrical tape.
There's a large flat diffusion layer behind the LCD that diffuses the light from the lamp evenly across the screen. We want the lamp to be directly illuminating this diffusor, rather than the LCD itself.