Acrylic is quite easy to get scratches, so you must take extra care when cleaning it.
Blow off any surface dust and dirt. Running water over the plastic sheet to float off the remaining dirt and dust. Repeat this process until your acrylic looks clean. Don't scrub with the cloth, or you will scratch the surface.
Make a mild cleaning solution to get rid of stubborn dirt and dust. Combine some mild dishwashing liquid or laundry detergent with some lukewarm water. Pour this solution into a spray bottle. Spray the cleaning solution onto your acrylic. Gently wipe it off with soft and clean cloth, constantly turning or rinsing the cloth so that you always wipe the sheet with a clean section of material. Repeat these steps until your acrylic looks smooth and glossy. Don't wipe your acrylic with a dirty cloth because it will scratch the surface.
Clean your acrylic product whenever you notice dust or dirt on the surface. Never use paper towels because the coarse fibers can scratch and streak the surface.