Seal the porous mosaic tiles before you install them on the backsplash. Because you do not want excess sealer running down the sides of the tiles, you need to use a spray-on sealer. Thus, you can coat the tile with a light mist; applying too much will drip down the sides, keeping the grout from sticking to the tiles. Use a light coat only.
Grout the installation as you would normally for any other tile installation. Put a pile of grout on top of the countertop against the backsplash. Use the grout float to push that mud up and across the face of the mosaic tile backsplash. Push the grout in multiple directions and work your way from the bottom up. Let the grout sit for at least 20 minutes before washing.
Fill a bucket with room temperature or cold water to clean the grout from the backsplash. Dampen the sponge and lightly rub it across a section of the mosaic tile. Smooth the joints while at the same time removing grout from the tile. Rinse the sponge out when it gets dirty and continue washing until you are finished.