First, check the bulb (I know, that sounds obvious)
Second, check the fuse (Yeah, that's obvious, too)
Also, when checking 1 and 2 above, also check them with a voltmeter to make sure you're actually getting voltage to the bulb.
Third, check the ground connection to the back-up light housing - it might have corroded or sumthin.
Lastly, the back-up light switch is located at the front of the transmission on the top, front corner of the passenger side, in about as difficult a place (but not impossible) to replace it as can be. It will have two or three terminals on it. The wires must be removed before removing the switch, which has a hex body to accept something like a 22mm or 7/8" wrench/socket.
If you replace it, remember to put thread sealant on the threads before putting the new one in.