Cut the scrap lumber into pieces sized for the desk’s construction using a circular saw. Cut one piece so it's 36 by 20 by 1 inch for the top. Cut two pieces of 30 by 20 by 1 inch and one piece that's 36 by 31 by 1 inch for the back. Sand all sides of the four pieces with medium-grit sandpaper to remove rough edges.
Place the top piece on your work surface, resting it on its longer 1-inch-wide side. Place the two side pieces at both ends of the top piece. Rest the 1-inch sides of the side pieces against the top piece, making sure the edges are flush. Apply wood glue where the pieces meet. Hammer 2-inch nails through the top of the top piece into the 1-inch edges of the side pieces. Place one nail every 5 inches for a total of four nails per side piece.
Place the back piece of wood on top of the side and top piece. Line up the edges and apply wood glue where the pieces meet. Hammer one 2-inch nail every 6 inches around the edge of the back piece into the 1-inch sides of the top piece and side pieces.
Fill the nail holes with wood putty. Let the putty dry according to manufacturer’s directions. Once the putty dries, paint or stain the surface of the desk. Let the paint or stain dry overnight before setting it up on the side pieces and using the completed desk.