Examine the wall. The wall should be in good condition. If it is not, repair it prior to installing the backsplash.
Mark starting and ending layout lines on the kitchen backsplash. These lines will be where the backsplash starts and ends. They will help you determine where to cut your backsplash pieces to size. Mark the lines with a pencil and long level.
Spread white latex-modified thinset mortar on the kitchen wall at the starting line of the backsplash with a notched trowel.
Press the mosaic tiles that are mounted on the paper into the thinset mortar. Start at the bottom of the backsplash and work up. Place a wooden block over the tiles and gently tap the block with a hammer to even out the tiles in the mortar. Cut the paper on the mounted tiles with scissors to cut the sheet to size. If needed, trim the mosaic tiles with tile nippers. Let the tile cure for 20 minutes.
Remove the paper from the front of the mosaic tiles. Wet the paper with a damp sponge. The paper should be wet for approximately 10 minutes. After 10 minutes, you should be able to simply pull the paper off diagonally, working carefully not to pull up any tiles.
Examine the backsplash to see if there are any tiles that are chipped or cracked that need replacement. Remove them with a screwdriver, apply more thinset mortar to the space, and push new tiles into place. Let the tiles dry overnight.
Apply non-sanded grout to the tiles with a grout float. Hold the grout float at a 45-degree angle to get the grout into the tile joints. Remove the extra grout from the tiles by moving the float over the tiles diagonally. Use a damp grout sponge to remove the residue from the tiles. Allow the non-sanded grout to dry overnight.
Caulk the space between the backsplash and the countertop. With a caulk gun, spread a bead of caulk along the gap between the two surfaces. Spread the caulk smooth with your finger. Let the caulk dry overnight.