Use a solution of mild detergent, not dishwasher detergent, or soap and warm water. If it is needed, use a solvent-free, grit-free soft cloth to loosen dirt or grime. Do not scour. Do not use abrasives. Rinse with clear warm water. Blot the surface dry. Use a soft, clean cloth such as a clean cotton cloth diaper or towel.
While the acrylic may look like glass and be smooth like glass, it is not glass. Chemical cleaning agents including acetone, alcohol, ammonia, benzene and lacquer thinner may have uses on other surfaces but they are likely to damage acrylic. Even mild cleaning agents such as window cleaner could injure acrylic surfaces.
Additionally, there are commercial products available for specific brands of acrylic. Check the manufacturer's cleaning instructions for the acrylic product you have, and determine whether the manufacturer has a specific recommendation.
To dust acrylic surfaces, try using a damp chamois or dampened soft cloth. Wipe gently. If there is a grain or pattern, wipe in the direction of the grain. Avoid rubbing and causing friction. If you press too hard or grind against the surface, you are likely to leave marks. Do not use paper towels. The fibers in the paper can scratch acrylics.
To protect acrylic surfaces and to remove rust, juice, ink or dye stains, you may be able to use an automobile paste wax of extremely high quality. Do not use a cleaner-wax as it is likely to damage the acrylic. For safety, be sure to test a small, inconspicuous area in case damage occurs. Remember that some waxes and other polishing agents contain petroleum. These products can harm the surface of the acrylic item. Spray waxes in particular should be avoided.