To build a Murphy wall bed, assemble the mattress box using plywood. Make the bed fold into a frame in the wall, or build the frame out of plywood yourself and attach it to a wall.
To make a frame out of plywood, fasten two plywood sides to a plywood bottom, making a box. Then, fasten back supports to the box and a front support at the top. Add side trim at the front of the sides and to the top of the sides. The next step is to add the front top trim and the top back trim, which should be left with an overhang at both ends. Finally, the top is attached with the same overhang as the top back trim.
Make the mattress box by attaching the sides, which are cut at a diagonal, and back to a plywood bottom. Add decorations to the face of the mattress box. Once they dry, use hinges to attach the wall box to the mattress box, and to keep the door from falling open, use a clasp. Finish making the Murphy wall bed by filling nail and screw holes with wood filler and finishing them as desired. To install the bed to a wall, use screws to fasten the support boards into a stud on a wall.