Turn off the circuit connected to the light fixture you are working on to avoid electrical shock. Never work on a light without first cutting the power to it.
Remove the plastic cover over the lights. This cover is brittle, so work carefully to avoid cracking it. Set it aside in a safe place.
Remove the existing T12 bulbs. Give them a quarter turn to disengage them and then pull them down gently. Dispose of these lights according to your local regulations.
Cut the wires running to the existing ballasts. Make the cut as close to the ballasts as you can get. You will use these wires to connect the lamp to the new ballast.
Unscrew the screws holding the ballast in place. Keep one hand on the ballast to avoid dropping it on your head once the screws are removed. Dispose of the ballast according to your local regulations.
Screw the new T8 ballast into the same position as the old ballast.
Follow the instructions that came with the ballast to wire the new ballast to the light fixture. Secure the connections with electrical tape.
Install the new T8 bulbs. Though these bulbs are thinner, they will fit in the existing fixtures.
Replace the plastic cover by snapping it into place. Again, work carefully to avoid damaging it.
Turn the power that runs to the fixture back on.