How do you replace a fog light on a 2005 Camry XLE? The owners manual says to take it to the dealer.

The entire light assembly or just the fog lamp bulb?
The assembly requires removing the bumper...

Actually, the outside portion of the light assembly is loose. The center side (closest to the middle of the car) is still attached. I just wanted to get to light to try and re-secure the side that is loose. I read in a repair book that the car needs to be jacked up and the tire removed to access it from the backside of the bumper in the wheel well. Is this true?

It's worth a try but I'm not certain if you will gain sufficient access.
Let us know and good luck.