Cover the existing hearth with a thin layer of mortar. Apply the mortar over the existing hearth with a notched trowel at about a 1/2-inch thickness.
Allow the mortar to dry for 24 hours.
Apply a layer of mortar to the back of a rock. Position the rock at the front center of the hearth. Set additional rocks onto the hearth, working in an outward and upward fashion. Position the rocks so that there is about 1 inch of space between them.
Cut any rocks that need to be sized to specific locations with a chisel and a hammer. Measure the area where the rock needs to be fit with a measuring tape. Transfer the measurement to the rock, using chalk to mark out the dimension. Set a chisel of the chalk mark. Bang a hammer into the back of the chisel to break through the rock.
Allow the rocks to set for 12 to 24 hours.
Fill a grout bag with heat resistant grout. Squeeze the bag to apply the grout between the spaces of the rocks.
Run a stick over the grout to smooth it out, making a natural look.