Lay out the sheets of mosaic on the kitchen counter in front of the backsplash. Practice placing the sheets next to each other to help determine how much space should be between the sheets to help the grout lines blend together into a seamless application.
Slice through the mesh on the backs of the tiles using a razor blade to trim the sheets down to the appropriate size for the space. Cut any individual tiles to fit the edges of the installation using tile nippers.
Spread thin set mortar onto the backsplash wall with the trowel. Spread the mortar to the correct depth using the grooved edge of the trowel. Flip the trowel over and smooth out the lines left in the mortar by the trowel. This will help prevent excess mortar from coming up between the small tiles.
Press each sheet of mosaic onto the wall from the bottom up. Smooth the sheet upward into place with the flat of your hand. Adjust the spacing of the sheets by pushing them slightly with your hand.
Place the flat board on top of several sheets of mosaic at a time and tap it lightly with the rubber mallet. This will help embed the mosaics into the mortar. If your tile sheets come with a paper film over them to assist with installation, moisten the film lightly with a damp sponge to soften the adhesive. Then peel the paper film carefully off of the tiles, and adjust any tile that might be slightly out of line using your fingers.
Allow the mortar to dry for 24 to 48 hours after installing the tiles. Spread grout over the entire surface of the backsplash with a grout float. Move the float from different angles to help ensure each of the grout joints is filled adequately.
Wait 10 minutes for the grout to begin to harden. Clean off the surface of the mosaics with a lightly dampened grout sponge. Work the sponge in circles over the entire backsplash, rinsing it out frequently until all excess grout has been cleaned from the surface of the tiles.