Switch off the circuit breaker on the line you are connecting your new fixture to. Use a ladder to locate the joists in your ceiling closest to the installation spot. Use your stud finder to locate the joists and your pencil to mark the position of both edges.
Remove the existing light fixture and disconnect the power wires inside. There should be two connections inside the old fixture, held together by a combination of electrical tape and wire nuts. Unravel the tape to expose the nuts, then turn the nuts counterclockwise to loosen and remove them. Pull the wires apart and set the old fixture aside.
Ask a helper to hold the light fixture up to your ceiling at the mounting location so that the screw holes in the back panel of the fixture line up with your ceiling joist locations. Press the tip of your pencil into each screw hole and mark its location on the ceiling. Remove the light and use your power drill to make pilot holes into the ceiling joists at each pencil mark.
Hold the fixture up to the ceiling again and use your screw gun and mounting screws (included) to fasten it in place. Find the metal tabs on the back wall of your fluorescent fixture base. Use your flat-head screwdriver to pry out at least one tab through which the power wires will run.
Slide the two power wires that run from the ceiling-mounted junction box through the vacated tab location and attach them to the corresponding wires inside the fixture. Install a rubber shield or grommet along the inside edge of the tab opening to protect against wire wear. Twist each set of wires together and use wire nuts to tighten and cover the joint. Wrap the nuts and about 1 inch of rubber sheathed wire with a few layers of electrical tape.
Attach any covers, trim or ballast shield that your particular fixture may require. Use your screwdriver to tighten the fasteners included with your fixture. Insert your T8 fluorescent light bulbs into the sockets at each end of the fixture and twist them so they lock in place.
Insert the plastic cover over your open light fixture and slide it into position so the locking tabs engage at each end and along each side. Turn the circuit breaker back on and test the light.