Sweep the slate floor to remove any dirt or dust. Mop a wax remover onto the surface of the floor, if the slate has an existing wax coating. Only apply the wax remover to a 4-foot-by-4-foot section of the floor.
Let the wax remover soak for the amount of time directed on the package. Meanwhile, rinse the mop in clean water. Once the wax is softened, mop it up with the clean water.
Continue the wax removal on the rest of the floor, working on one 4-by-4-foot section at a time. Apply the wax remover, let it sit, then mop it off.
Mop the floor again with a neutral-pH slate tile cleaner. Rinse the floor with clean water. Let it dry for three days.
Pour the slate sealer into a paint tray. Roll a paint roller into the sealer to wet it, then apply the sealer in a thin, even layer across the slate floor. Start in the corner farthest from the door, and overlap your edges as you apply it.
Let the first coat dry according to the directions on the package. Apply the second coat perpendicular to the first, then let it cure for 24 hours.