Sand and dirt are abrasive and will scratch your marble floor, so be sure to dry dust mop frequently. You can vacuum as well, but check for wear on the wheels and attachments, as these can also scratch the floor.
For regular cleaning, simply use a damp, soft cloth. You can use a mild detergent, such as dishwashing liquid, a couple of times a year for heavier soiling. Rinse thoroughly and wipe dry. Do not use detergents containing even mild acids, such as vinegar or lemon, as these will etch the surface.
Avoid soap scum build-up by wiping your shower area with a squeegee after each use. You can also use a mixture of ammonia and water (half a cup of ammonia in a gallon of water), but ammonia can dull the surface of the marble, so you'll want to use it infrequently. Soap-scum remover is also effective---check the label to make sure it is nonacidic.
Simply turn your hose on outdoor marble. You can use a mild bleach solution (half a cup of bleach to a gallon of water) to remove algae.
You can purchase a commercial marble cleaner and polisher to return the luster to your marble. Companies that sell marble often stock imported cleaners, which are safe to use on even imported marble, which is softer than U.S. marble.
Organic stains---those left by coffee, leaves or bird droppings---will generally disappear with exposure to sun and rain. If the stain is inside, you can use a 12 percent hydrogen peroxide solution with a few drops of ammonia. Dissolve oil-based stains (cooking oil or cosmetics) with a mild liquid cleanser that contains bleach, and then rinse and wipe dry. You can buff water spots and fine scratches out of the marble using fine (0000) steel wool.