Stand up two 1/2-by-6-by-12 side boards on their small ends. Make them parallel to each other about 3 feet apart with an assistant's help. Suspend a 1/2-by-6-by-36-inch top board across them so that the ends of the top board line up with the outside surfaces of the side boards.
Drill two holes down through the top of the top board so that the holes penetrate each of the side boards, for a total of four holes. Place 2-inch wood screws in the holes and tighten them fully. Flip the boards over and attach another 1/2-by-6-by-36-inch board to the bottom to serve as the bottom board.
Turn the unit on its side so that there is a rectangular opening facing upwards. Set a 1/2-by-13-by-36-inch rear board over this opening and make sure it is even all the way around its edge. Drill holes every 8 inches through the rear board and into the boards below. Place 2-inch screws in the circle of holes and twist them in completely with the drill.
Position two 1/2-by-1-by-36-inch boards parallel to each other with their largest sides on the working surface. Move them 11 inches apart. Set two 1/2-by-1-by-11-inch boards perpendicularly between the long boards and move them to the edges so the four boards form a rectangular frame.
Drill two holes at each joint, with one hole in each of the adjoining boards. Insert a peg in one of the holes, spread a thin line of wood glue on one of the surfaces and peg the boards together. Allow four hours for the glue to dry. Repeat this process to build a second frame of the same size and set it aside.
Arrange two 1/4-by-1/2-by-35-inch boards and two 1/4-by-1/2-by-13-inch boards on top of the frame so that they make an upper level of rectangular frame. Position a 1/4-by-12-by-35-inch glass pane within the upper frame, supported by the lower frame. Arrange the pieces to make sure that the frame is functional. Remove the glass frame and glue each of the upper frame pieces to the lower frame with a thin bead of wood glue. Allow four hours for the glue to set.
Reposition the glass pane within the frame and place the second premade frame over the glass pane. Adjust the positioning to make sure it is even all the way around. Drill holes through all three frame layers, every 6 inches, making sure the drill doesn't catch the glass by accident. Secure the layers together with 1-inch wood screws.
Set the cabinet on the working surface with the rear board touching the working surface and a rectangular opening facing upward. Hold the door up to the cabinet and position two hinges between the door and the cabinet. Mark the positions of the hinge holes and drill at each marking, being careful not to drill all the way through the 1/2-inch thick framing board and into the glass pane. Attach the hinges to the door and the cabinet with 1/2-inch wood screws.
Find the studs in the wall using the stud finder and mark their locations. Hold the gun display box over the wall with the rear board against the wall, the glass front facing out and the hinges on the top side of the box. Drill four evenly spaced holes through the rear board and into the wall where the studs are, positioning the holes in two rows. Attach the display box to the wall with 3-inch wood screws.