Clean the area well with an all-purpose cleaner and old clean rags. Eliminate any food particles, dust, grime and loose paint while you clean.
Tape off the area you'll be painting for the backsplash using the 1-inch painter's tape. Protect the counter top with a drop cloth or newspapers.
Paint the entire backsplash area with a medium nap roller brush using the grout-colored paint. Apply two coats of this paint and let it dry completely, for about 4 hours.
Transfer your tile design sketch to the newly painted wall using a pencil. Use a ruler to ensure the lines are straight and the distance between them is realistic and consistent.
Cover the lines of your tile design with one-eighth-inch painter's tape. These lines will protect the grout-colored paint from the drywall compound and from being painted over.
Put drywall compound over the backsplash area using a drywall trowel. Keep the compound as smooth as possible while still allowing for some texture to mimic a ceramic tile surface. Remove all painter's tape immediately after you finish so it won't become trapped under hardened compound.
Allow the drywall compound to dry completely, for about 24 hours. Use a damp cloth to smooth out any rough areas from the compound. Re-tape the outer edges of the backsplash area and the grout lines with new painter's tape.
Paint two coats of primer over the tiles using a medium nap roller brush. Allow it to dry completely, for about 24 hours.
Apply paint to the faux tiles in the colors and density you desire. Use a sponge to mimic the muted, blended colors of ceramic tile. Allow the tiles to dry completely, for about 24 hours. Apply a clear finish, either a matte or glossy version, depending on the look you desire.