Sand the surface of the existing counertop using an electric sander with a medium-grit sanding belt.
Clean the sanded surface using a vacuum with a brush attachment to remove any dust caused by the sanding.
Spread a 1/2-inch-thick layer of mortar over the surface of the countertop using a trowel.
Scratch the surface of the mortar using a mortar rake to create grooves in the mortar.
Press faux-slate tiles halfway into the mortar, spacing each tile 1/4 inch apart. Arrange the faux-slate tiles so they are lined up evenly across the countertop. Let the mortar dry for 10 to 12 hours.
Spread a 1/4-inch-thick layer of medium grout over the faux-slate surface using a trowel, then scrape off the grout to spread it in between the tiles and to remove any excess grout.
Wipe off the surface of each slate-like tile using a damp sponge. Allow the grout to dry for 10 to 12 hours.
Put on a protective face mask. Paint a layer of clear latex sealant over the entire surface of the faux-slate countertop using a 2-inch flat paintbrush, then allow the sealant to dry for six to eight hours.