A fluorescent light is a tube filled with a gas that creates light when electricity is run through it. The ballasts on the sides of the fluorescent tube control the intensity of the electricity that flows through the bulb to excite the mercury vapours. When the ballasts are malfunctioning the light may flicker or make a loud buzzing sound. Testing may be necessary to determine if the ballasts are bad and need to be replaced.
Check to make sure there is power going to the light fixture before doing further troubleshooting. Inspect the fuse box for the room to make sure the room is receiving electricity.
Inspect the bulb, looking for dark spots near the ends. Dark spots indicate that the bulb is faulty and needs replacing.
Touch the probes of your multimeter against the two pins coming from the end of the light to check whether there is continuity between the two. If there is no continuity the electrodes are bad.
Place the fluorescent bulb into a fluorescent fixture you know works if the above tests do not indicate that the bulb is bad. There may be a gas leak which cannot be detected. Replace the bulb if it still doesn't work.
Open up the containment portion of the fluorescent fixture to expose the ballast. Look for leaking oil. Leaking oil means the ballast should be replaced. Hold a multimeter to the high voltage side of the ballast (indicated on the wiring diagram on the ballast) and test for continuity. Replace the ballast if there is no continuity.