How do I replace the back light in the Delco CD-Radio unit?

Take the radio out. Follow a Repair guide, you can get one at a auto parts store. Once Radio is out take the face plate off. Then remove the screws that hold the circuit board on. Then you will need to desolder the bulbs they will be small 3mm bulbs looking like LED's. You will need to get 12 Volt to replace them with. I got mine at a electronics supply shop. You ant to get something that looks kinda like this. 12V 35mA Micro Lamp

There is a simple twist in bulb for the backlight: ACDelco 16208443 GM Original Equipment Multi-Purpose Light Bulb, I found mine on Amazon, you can get them at most GM dealers for a buck or 2 more if you don't want to wait.

The trim around the radio just pops off, held in by a few clips, a small flat blade screwdriver slipped between the trim and the dash will lift it enough to get a grip with your fingers, then just pull gently, the trim ring around the ignition will also pop off, separate piece.

Once the trim is off, there are 3-4 screws holding the radio unit in, remove them and slide the radio forward enough to reach behind and undo 2 wire connectors and the antenna cable.

The faceplate is held on by a few plastic clips that snap onto the radio chassis, gently pry these up with your small screwdriver and the faceplate should come free with the small circuit board holding the build attached, twist out, twist in the new one and reassemble. Took me about 15-20 minutes total.