Cover the installation surface with a layer of plastic sheeting to conceal the wall studs or plywood. You can skip this step if the wall is made of concrete. Cut the plastic sheeting to fit with the utility knife and staple it to the wall with a hammer tacker.
Measure the backer board to fit and cut the pieces as necessary with an angle grinder. Install them on top of the moisture barrier. Place them against the wall and nail them on with the nail gun. Stagger the sheets so that there are no identical joints running up the wall. Caulk the joint between the vinyl siding on the adjacent wall.
Mix up some thin-set mortar in your bucket with the drill and paddle until you achieve a thick, creamy texture. Use the highest speed on the drill. Follow the instructions on the bag with regard to how much water is needed, as different sized bags have different requirements.
Start at the bottom of your wall and work your way up so you can stack the pieces. Use spacers between the pieces to keep relatively same-size joints as you work. Spread a layer of thin-set mortar onto the installation surface with the notched trowel and press the stones into the mortar.
Make any necessary cuts with the tile wet saw. Allow at least an eighth of an inch to a quarter of an inch of space where the stone veneers terminate against the vinyl siding. This space is necessary to allow for seasonal movement between the two surfaces. Let the installation dry for 24 hours.
Remove the spacers and mix up some grout in the bucket. Use the lowest speed on your variable speed drill (under 300 RPM). Similar to the thin-set mortar, add an appropriate amount of water based on your container of grout. Put the grout into the grout bag.
Insert the tip of the bag into the joints between the stones. Squeeze the bag to fill the joints. Let the grout sit for 20 minutes and then smooth the joints down with a damp sponge. Rinse the sponge out frequently with clean water in a bucket. Caulk the joint against the vinyl siding to finish the installation.