Locate the wall studs that will support the rock wall with a stud finder. Snap a chalk line on the drywall over each stud.
Determine the width and height of the rock wall behind the wood stove. Score sheets of cement backer board with a utility knife and snap them on the corner of a work bench to fit the width and height of the rock wall. Secure the backer board to the drywall with 4-inch wood screws, using an electric screwdriver, along each wall stud at 4-inch intervals.
Spread thinset mortar on the back of a section of stone veneer with a trowel. Place the stone on the bottom of the wall at one corner. Place a section of 2-by-4-inch lumber over the stone veneer and tap it into place with a rubber mallet.
Continue installing stones along the bottom of the backer board to complete the first course. Add additional courses until you have completed the rock wall.
Press grout between the seams of the stones, and along the edges of the cement backer board, with a grout float. Wipe away excess grout with a damp sponge.