Put on your eye protection. Turn off power to the room where you are working. Lay down a drop cloth. Set up the ladder.
Remove the cover of your existing light fixture. Use pliers to remove the nut securing the cover if it is hard to loosen by hand. Remove the light bulbs.
Remove the screws holding the light fixture's backing plate to the ceiling. Use the electrical tester by holding one lead to the hot, or black, wire and one lead to the ground wire, which is usually green. This way you can make sure the power is really off. Unscrew the wire nuts, noting where each wire connects.
Remove the backing cover from your fluorescent strip light fixture. You will see several holes in the top of the fixture; these are screw-mounting holes. Place the fluorescent fixture on the ceiling, with someone to help hold it there. Level the light and mark two screw hole locations though the openings, using the permanent marker.
Mark the hole that will allow your electrical wires to come into the fixture. Punch out the metal plate in the top of the florescent light fixture, using the scratch awl and hammer. Your wires will come through this hole.
Take down the light fixture. Make holes in the ceiling on your marks, using the scratch awl. These holes will hold the anchors that will hold up the florescent strip light fixture. Insert the ceiling anchors. Hammer them into place.
Lift your light fixture to the ceiling again, using an assistant to help you line up the two anchor holes. Pull the electrical wires though the hole you previously punched out of the light fixture. Place the mounting screws through the light fixture holes and into the ceiling anchors. Secure them, using the screwdriver or a screw gun and driver bits.
Hook up your wires. Review the notes on how the old wires were hooked up and do the same, matching the wire colors between the fixture and the house wiring. Twist each pair of wires together and screw a wire nut on their ends.
Install the backing cover on the fixture by pressing it into place on both sides. Insert the fluorescent bulbs into each socket end and twist slightly clockwise until they tighten.
Install the outside decorative light cover. Turn on the power and test the light to make sure it functions properly.