Pour latex modified thinset for glass tiles into a bucket, and mix with a drill and a drill-mixing attachment, following the manufacturer's directions.
Scoop about a cup of thinset out of the bucket with a trowel. Spread the thinset on the wall in straight lines, using the notched side of your trowel. Apply the thinset one small area at a time. The thinset dries in 10 to 15 minutes, and you need to get the tile on the wall before it dries.
Use the smooth side of the trowel to flatten the notches and smooth the thinset.
Hold a tile sheet in your hand, and apply a thin layer of the thinset to the mesh-backed side of the glass tiles with the smooth edge of the trowel. This step will provide better adhesion. It will also keep the mesh from showing through the tile.
Press the tile sheet onto the thinset on the wall. Use a grout float to press firmly on the tile sheet to help it adhere to the wall. Continue applying thinset to the wall and tile, making sure to line up joints and grout lines, until the backsplash has been completely covered. Let the thinset cure 24 to 48 hours.
Mix your grout, with the drill and mixing attachment, following the directions on the package.
Use a grout float, held at a 45-degree angle, to push the grout into all of the joints and lines. Remove excess grout with the edge of your float. Let the grout cure for 20 minutes.
Dampen a sponge with water, and wipe any remaining grout residue from the face of the tiles.