If you have a light fixture above your shower, you will notice that it has a sealed lens that protects the bulb from water and other moisture. This measure is necessary since water and electricity do not mix well at all. When the bulbs of these fixtures need to be replaced, you'll have to dismantle the fixture slightly to access the bulb. While it may look complicated, these fixtures are made to be disassembled quite quickly.
Set up a ladder under your shower fixture. Depending on your ladder, you might want to place cardboard down in your shower to prevent abrasions.
Climb the ladder and locate the trim ring on your shower fixture. Grasp this trim ring and pull it off while twisting slightly.
Unscrew the light bulb from the shower fixture by turning it counterclockwise. Replace it with an appropriate replacement bulb and screw this bulb into place by turning it clockwise.
Push the trim ring back into the shower fixture. It should snap into place once pushed in all the way.
If the bulb recently burnt out, it may still be warm or hot. Allow to cool for several minutes before touching it.