Weld the trough onto the backing so that the backing is sitting inside the back of the trough. Use water-resistant welding materials. Weld the tubing so that it sits just an inch above the bottom of the trough on both sides, tucked into the corners. The tubing runs from the trough, all the way up the sides of the backing, and into the upper trough. Weld the tubing against the edges of the backing. Weld the upper trough into place mirroring the lower trough. This trough will disguise the water hosing and the lighting fixtures (if any)
Line the bottom trough with waterproof lining to 1/8-inch below the upper edges of the trough. This ensures a watertight seal. Drill a hole into the back of one of the metal tubes one inch above the trough. This hole should be large enough for the power cord from the pump to fit through.
Decorate the backing with slate, copper, waterproof mirror materials or stainless steel. Use patterns that will guide the water down over the backing and into the trough in a visually and auditorily appealing way. For inspiration, peruse water feature magazines, books or websites. Glue or weld the backing decoration of your choice into place with waterproof adhesives or welding materials. Check all seams at this point with a flashlight in a dark room to find gaps. Seal any gaps.
Set the pump into the trough. Run the power cord up the tube with the hole in it and out the hole in the back. Run the outflow water tube up the other metal tube and through the opening in the trough above. Attach this tube to a fitting designed to run water evenly over your backing, or simply arrange it over your decorative backing so that the water flows over it the way you envisioned it should. Glue the hose into place as necessary with waterproof glue.
Install lighting in the upper trough if you wish, placing and angling the bulbs so that the fall of the water over the backing is on display. Cut a hole in the back of the upper trough to run power cords through it.
Mount your wall fountain to the support beams in the wall, or, if it is tall enough, simply set it on the floor against the wall and fasten the upper trough to the wall from the inside back portion with screws so that the wall fountain does not tip with its own weight.