Turn off the power leading to the light fixture's circuit at the circuit breaker panel. Remove the cover to the light, and take out the tubes.
Cut the wires leading to the current ballast as close as possible to the ballast, using a set of wire cutters. Loosen and remove the screws holding the old ballast in place, and remove the ballast from the lamp.
Remove 1/2 inch of insulation from the ends of each of the wires you cut in the previous step, using a set of wire strippers.
Match the colors of the existing lamp wiring to the colored wires of the new ballast. Slip a wire nut over the bare ends of each wire pair, and twist it until it's holding the wires tightly in place.
Wrap a short piece of electrical tape around the base of each of the wire nuts and wires leading into them for extra security.