Why won't my bathroom light fixture work?
If you have a multi-meter and feel comfortable poking around, you can find out some preliminary info. Take off the face-plate for the switches and check the voltage between the two screws on the light switch. You should see nothing when it's on, and full voltage (120/230/etc) when it's off:


If you see no voltage all the time, then there's likely a power problem feeding the switch.
If you see full voltage all the time, then the switch is probably broken and can be easily replaced.
If you see no voltage (switch on) and full voltage (switch off), then it's probably the light fixture.