One of the advantages of coating your garage or utility room floor with a super-hard resin like epoxy is that cleaning it is a breeze. You can't use just any cleaner, though. Acidic cleansers, such as vinegar or lemon juice, can etch the finish and dull it, and strong alkaline cleaners, such as ammonia, can be equally damaging when used in a concentrated form. The good news is that you seldom need anything stronger than mild detergent. Epoxy isn't indestructible, so you should always avoid brushes with hard bristles when you need to scrub.
Sweep the floor with a broom, or, if the floor is in a garage or utility area, clear the dirt with a blower. If it has been a while since you cleaned your garage or utility room floor, you may want to spray water over it prior to mopping to loosen caked-on dirt.
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Scrape off any large dirt deposits that don't loosen with water, using a plastic paint scraper or a squeegee. If you use a squeegee with a metal frame, ensure the corners of the frame are rounded, and avoid using scrapers with metal blades; metal can scratch the finish.
Prepare a cleaning solution by mixing 1/2 cup of mild detergent, such as all-purposed household cleaning detergent or dish detergent, in a gallon of hot water. Because it is mild, dish detergent is recommended. You can also use a weak ammonia solution -- 1 or 2 ounces per gallon of hot water.
Mop the floor with a string or a sponge mop. Spread the cleaning solution liberally, then use the mop to rub dirt out of the floor. If you need to scrub, use a brush or push broom with moderately stiff plastic or fiber bristles.
Wring out the mop and dry the floor with it, rinsing the mop again with clear water to remove soap residue. Mop up excess water; then allow the floor to dry completely before walking on it.