Sand the surface of the kitchen walls using an electric sander with a fine-grit sanding belt. This will remove any roughness and create an even, smooth surface.
Vacuum the wall and surrounding areas using a shop vacuum to remove any dust and debris.
Spread a 1/2-inch thick layer of fine grout over the entire wall using a trowel.
Press flat, 1/4-inch thick stones halfway into the grout-covered wall. Space each stone 1/4 inch apart.
Scrape the trowel over the stone wall to spread the excess grout over the areas with too little grout.
Wipe off the surface of each stone with a damp washcloth and run your finger along each grout line to make the lines smooth. Allow the stone kitchen wall to dry for 24 hours.
Paint a thin layer of waterproof stone sealant over the wall and allow the sealant to dry for eight hours.