Sweep the slate tiles. If they are on the ground, sweep them often to remove dirt so that it doesn't grind into the surface, making it look dull.
Mop the tiles with warm water to keep them free of possible stains. Occasionally use a mild dish soap when mopping. For tiles on the sides of a house, use a water hose to wash them off at least twice a year.
Brush on a slate tile sealant over the tiles. Use a paintbrush or paint roller, depending on whether the surface is smooth. Apply the sealant in layers, letting each coat dry for an hour before applying the next coat. You want at least three coats.
Check the stone for absorbency annually. Pour a glass of water on it to see if it beads up. If the water absorbs into the stone within an hour, it is time to reapply the sealant. Always strip off the old sealant before brushing on the new. Use a water-based stripper for water-based sealants, and a solvent-based stripper for synthetic sealers. Brush it on with a paintbrush and let it sit for the time recommended on the packaging. Scrub with a scrub brush and more stripper to remove.