Some good ways to clean a fiberglass shower are to use non-abrasive cleaners, such as mild dishwashing detergent, a paste made from baking soda and water or an all-purpose cleaner, notes the University of Nebraska-Lincoln. Because a fiberglass shower or bathtub can scratch easily, cleaning tools such as sponges and brushes should be non-abrasive.
For a general cleaning of a fiberglass shower stall, a mild detergent can be applied with a sponge to the shower and then rinsed thoroughly to remove any traces of the detergent. If the shower has a few stains, then apply a paste made from baking soda and water, rub in the paste gently with a sponge and rinse thoroughly, states the Old Farmer's Almanac. If there are tougher stains, such as old paint on the shower, then applying some acetone or turpentine on the stain may be helpful.