Check the light switch to ensure it is in the off position.
Remove the diffuser in the fixture. Push up on an angle until the diffuser clears the ridge that it sits on.
Put on work gloves. Gently wiggle the fluorescent tube to ensure the problem is not a poor contact. Twist the fluorescent tube 1/4 turn clockwise, you will feel the tube come free. Slide one side of the tube straight down 6 inches. Gently pull to free the other side of the tube. Carefully dispose of the defective tube.
Hold the new fluorescent tubes horizontally so the electrodes on each end are vertical. Slowly slide the tube into the fixture until the electrodes hit the stop. Twist the bulb counterclockwise 1/4 turn until the tube locks into place.
Turn on the light switch to ensure proper operation.