Prepare the site for the front hearth. Remove any flooring finish or material necessary to expose the plywood subfloor, concrete slab or flooring substrate. Make sure that the area is clean and free of dust and debris.
Lay out the hearthstone without any adhesive to determine if any cuts will be necessary to achieve the desired size or appearance.
Cut the hearthstone to size using a a masonry saw, diamond saw or another tool capable of cutting the specific hearthstone material.
Position the hearthstone on the subfloor. Use a measuring tape to ensure that the stones are centered or otherwise aligned as desired. Leave 1/4-inch joints between each stone and between the stones and any adjacent material.
Trace around each stone, creating outlines, and remove the stones from their locations.
Apply adhesive liberally to the floor within the outlines you drew, and to the back of each stone, but put no adhesive within 2 inches of the edge of each stone. Use a polyurethane adhesive or another type of construction adhesive suited for use with the specific stone material and subfloor.
Press the hearthstones into place, making sure to leave a 1/4-inch gap between each stone. Set a level atop the stones to make sure they aligned correctly and make any necessary adjustments by pressing down on high spots.
Fill in the spaces between the stones with grout. If grout accidentally gets on the exposed top of the hearthstone, use a damp sponge to clean it off before it dries.
Run a bead of silicone caulk around the perimeter of the stones, placing the caulk between the stones and any flooring or other material type.