Turn off the power to the fluorescent light. When a ballast goes bad, it can generate a lot of heat; allow the ballast to cool down before you attempt to remove it.
Remove the fixture's shade lens, if it has one, and the three fluorescent tubes. To remove the tubes, twist the tubes in their sockets until you see the pins align with the slot. Then you can simply lower them out of their sockets.
Remove the cover that houses the ballast. In 3 lamp fixtures, this is usually on either side of the tubes. The cover can be removed by pressing one side to release it from its holding clips.
Use the touch-type voltage tester to check the black wire for voltage. If you don't get a reading, then you can proceed. If you read voltage, double check you have the correct breaker off.
Disconnect the black and white ceiling wires from the black and white ballast wires. Cut the red wire and the three blue wires as close to the ballast as possible.
Use the properly sized nut driver to remove one of the nuts holding the ballast in place. While holding the ballast up with your other hand, loosen the other nut. You will be able to slide the ballast out from under the loosened nut. Put the old ballast aside.
Insert the new ballast under the loosened nut. Use the nut driver to tighten up the nut that you removed. Tighten up the loosened nut to secure the ballast in place.
Use the wire strippers to strip about 3/4 inch of insulation from the ends of each wire you cut from the older ballast.
Wire the 3 lamp ballast the following way: The red ballast wire (one wire) gets connected to the red socket wires; the blue ballast wires (three wires) get connected to the blue socket wires, one to each socket; the white ballast wire gets connected to the white wire coming out of the ceiling; the black ballast wire gets connected to the black wire coming out of the ceiling.
Wrap a strip of electrical tape around each wire connector. Bend all of the wires so they are neatly bundled within the space allowed for them. Wrap the wires with a strip of electrical tape to help manage them.
Replace the ballast cover, tubes and lens.
Turn the circuit back on and test out your newly installed 3 lamp ballast.