Measure the space around the fireplace insert where you want the tiling to go and make a template of this area on the cardboard and on a piece of backerbaord. Lay the cardboard flat on the ground and place the tiles onto the template in the design you want to later transfer to the wall. Space the tiles with tile spacers and use the edge tiles along the outer border. Any tiles needing cutting leave to one side.
Score along the template lines of the backerboard with the utility knife, then snap the backerboard along these lines. Position the backerboard around the fireplace insert and screw in place with the backerboard screws and drill. Start with the corners first to get it in position, then one screw every 8 inches along the borders.
Mix a batch of thinset mortar, following the manufacturer's instructions. Starting at the bottom, apply a one-eighth-inch layer of mortar with the towel, about the size of two or three tiles. Furrow the mortar with the notched side of the trowel. Transfer the tiles from the cardboard template onto the mortar, pressing them gently in place, spacing with the tile spacers.
Apply more thinset, working along the bottom of the tiling area first, and then moving upwards in rows. Continue until only the edge tiles and tiles needing cutting remain.
Cut the tiles with the wet saw or tile cutters. If using a wet saw, wear goggles and dust mask and keep plenty of water on the blade as you gently push the tiles through the cutting edge. Mortar the back of the cut tiles and place them individually where they need to go. Set the edge tiles last of all, ensuring there is mortar along the 'V' of the edge tiles for good adhesive power. Let cure overnight.
Mix the grout as per the manufacturer's directions. Apply the grout to the tile joints with the grout float, keeping the grout float at a 45-degree angle to the joints. Sweep the grout into all the joints, then buff off the grout haze with a damp sponge or soft cloth. Let cure for three days before using the fireplace insert.