Sand the wall using an electric sander with a medium-grit sanding belt. This will remove any uneven texture and create a surface for the limestone tiles to adhere to.
Vacuum the area using a shop vacuum to remove sanding dust.
Spread a 1/2-inch-thick layer of mortar over the wall using a trowel, then run a mortar rake over the mortar to groove the surface.
Press limestone tiles halfway into the surface, spacing the limestone tiles 1/4 inch apart.
Spread a 1/4-inch thick layer of medium grout over the surface of the limestone tiles. Excess grout will become pressed in between the tiles.
Scrape the excess grout off the tiles, using the trowel. Wipe off the surface of each limestone tile using a damp washcloth.
Allow the limestone facade wall to dry for 12 to 18 hours.