Turn on the existing light to make sure that the circuit is working. Open the electrical panel and turn off the circuit breaker controlling the light circuit that you will be working on. Turn on the light after turning off the breaker to make sure that it is no longer receiving power.
Remove the screws that hold the light receptacle in place. Set the dial of a multimeter to 110 volts AC range and touch each terminal behind the receptacle with the tip of each multimeter prong to test for power. No reading in the multimeter indicates there is no power.
Loosen each terminal screw and disconnect each wire from each screw. Remove the light receptacle and straighten out the wires with needle-nose pliers. Splice each wire coming from the fluorescent light fixture on to the black and the white wires in any order, using wire nuts. Pull on each wire to make sure there is no loose connection.
Strip off 1/2 inch of insulation from the tip of a 6-inch green wire, using a wire stripper, and connect the wire to the grounding screw in the fluorescent light fixture. Splice the other end of the wire to the green or bare grounding wire running from the electrical outlet box, using a wire nut. Mount the fluorescent light fixture onto the ceiling, using screws supplied with the light fixture. Insert the fluorescent tube, then replace the fixture cover. Flip the switch to its "On" position to test the connection.