I couldn't find a good how-to for fixing the climate control light, so I took some pic's when I replaced mine.
Here's how I did it:
Remove the climate control module from the car. See other threads here on how to remove the dash.
Remove the 2 screws on the white tabs that hold the unit in the dash. <Image Below>
Remove the 2 electrical connectors from the back of the unit (1 Blue, 1 Black)
Remove the 2 round control knobs and the 2 slider knobs. <Image Below>
Remove the 4 small black screws from the back corners of the unit. <Image Below>
IIRC this is an SAE size nut.
Do not touch the screws on the black connector.
Pull the front (black) 1/2 of the housing from the back (white) 1/2 of the housing.
Once the black front is off you will see the circuit board. <Image Below>
You will see the light bubs to the right and left of the slider. <Red Arrow>
Press the white retaining clips to release the circuit board.
Flip the circuit board over and find the (2) terminals for the Bulb <Image Below>
I used Chem-wik to remove the solder from the terminals.
Once the terminal is de-soldered, remove the burnt out bulb.
Here is the replace bulb package from Radio Shack <Image Below>
Part # 272-1154
Install the bulb in the circuit board and resolder.
Put climate control unit back together and re-install.