Marble : Use a recommended proprietary marble cleaner on a soft lint free cloth to keep your planter clean and dust free.
Granite : Use a recommended proprietary cleaner on a soft lint free cloth to keep your planter clean and dust free. Alternatively, use a mild solution of dish soap and water and dry thoroughly with a clean soft cloth.
Never use a household cleaner on your planters, they may have acidic properties which react negatively to marble and granite.
Wood : If your planter has a wood surround it has been coated with OSMO UV protection oil. Recoat with this or another type of nourishing oil, as and when, you feel it needs it.
If you have chosen a tumbled stone planter, flick over the surface of the stone with a clean dry paintbrush or feather duster to remove dust and debris from the surface.