Dust off the acrylic. It is important to remove particles and debris so that the dirt isn't rubbed into the acrylic during the cleaning process.
Mix a small amount of mild dishwasher soap with warm water in a bucket. Never use glass cleaners or abrasive solvents on acrylic.
Clean the acrylic with a soft cloth dipped in soapy water.
Soak a clean cloth in fresh water and wipe down the acrylic in order to remove any soap residue. Soap residue can dull the look of acrylic once it dries.
Dry the acrylic using a soft cloth.
Apply an acrylic scratch remover to any areas where scratches are particularly noticeable. Novus is one brand of acrylic scratch remover that can be ordered online or found in home improvement stores. Acrylic scratch removers are typically applied using gentle buffing strokes, but be sure to follow the directions on the manufacturer's label.
Clean the areas where you applied the acrylic scratch remover with soapy water once again in order to remove any residue.
Wash the soapy water off with a cloth soaked in fresh water.
Dry immediately using a soft cloth. Evaporated water spots can dull the shine of acrylic.