Fluorescent light only one bulb out of two burning very dim

I like to start by swapping the position of the bulbs. If the one that didn't light, now does, it probably indicates a bad ballast (that long thin black "boxy thing" with wires coming out of it - it may be under a removable metal cover). Next replace the unlit bulb with a new one. If that doesn't light, try swapping the new light to the other position. If you still can't get two bulbs to light, replace both lamps with new ones. A good indication of a bad bulb is one or both blackened ends. The bulbs having two pins on each end have a small filament inside. This blackening is the metal of the filament "boiling off" and depositing on the glass. Eventually the filament gets thin and breaks so it doesn't provide the heat necessary to "prime"" the mercury inside the bulb that conducts electricity and excites the phosphor coating inside the bulb that emits light.If none of this works, most probably the ballast has "gone bad" and it, or the whole fixture, must be replaced, normally by an electrician. This can be done by the home "handyperson." You can cut the wires, remove the old ballast and replace it with a new one, splicing them to those of the same color from the new ballast using small "wire nuts." The one black and one white are the 120 volt power input wires. There are normally a pair of reds, a pair of blues, and a pair of yellows. Any wires of the same color are interchangeable. The blues and reds will go respectively to the bulb's sockets on one end of the fixture; the two yellows go to the opposite fixture end and are connected, in parallel electrically, to the other lamp sockets. If this makes sense, you may attempt to change your own ballast. If not, hire an electrician. Match the specifications for voltage, wattage, and number of bulbs, from your old ballast to the replacement - there are several different important electrical values to match even if the ballast looks physically the same size. Last, always turn off the electricity, and verify that it is safely off using a test light or meter before working on the fixture. Even though the black wire is normally energized and the white has zero volts measured with respect to ground, sometimes their function is reversed by an amateur where the wall switch may disconnect the black wire and make the fixture go off (as it should) yet the white wire remains dangerously energized, which is why you always test both of the wires with the test light or meter with respect to ground before touching any of them. Again, if this is not PERFECTLY clear, hire an electrician. Don't take chances, Electricity KILLS!