Prepare a wood-sheathed wall by stapling a waterproof membrane to the sheathing with a construction stapler. Cover it with metal lath, nailed with galvanized nails with a hammer at stud locations in the wall. Put metal flashing around windows and doors and install a "weep screed" of perforated metal at the bottom of the wall, under the lath and extending out at 90 degrees, so any water that gets behind the facing will drain out.
Mix mortar according to package directions and spread a layer about 1/8 inch thick over the lath, using a rectangular mason's trowel. Spread it evenly, then scratch the surface with the notched edge of the trowel, a stiff bristle broom or a leaf rake, to provide a rough surface for stone mortar to adhere to. Let this scratch coat cure a few days, keeping it slightly moist during the curing.
Dampen the scratch coat with a misting nozzle on a garden hose. Do this with a masonry wall, too, after installing any needed flashing. Lay a 1-inch base of mortar on the support ledge for real stone, but skip this for manufactured stone. Spread mortar on the back of the first façade stone, and set it in place at the bottom of one corner. Press it firmly into the mortar. If you're using regular shaped stone, use a level to make sure it is level.
Add other stones the length of the wall. Work in a triangular pattern with irregular shapes, adding bottom stones, then other stones on top to fit as you work across the wall. Install regular shaped stones in squares or rectangles like bricks; lay a course the length of the wall and add other courses on top. Adapt to the type of stone. Some will be cut in regular sizes, and others will mix square or rectangles of varying sizes.
Put corrugated metal ties into the wall and between mortar joints every 16 inches horizontally and vertically after the stone wall gets 16 inches high. Fasten these ties to the wall with galvanized nails or special concrete nails. Skip this with manufactured stone, which is light enough that it does not usually require wall ties.
Finish either natural or manufactured stone by cleaning excess mortar out of the joints between stones with the pointed tip of the trowel. Wipe wet mortar off the face of the stone with a damp cloth, or let it dry and brush it off with a wire brush. Complete the wall by putting cement grout into the joints. Use a cloth grout bag with a metal tip to force grout into the joint and smooth it.