Build the Legs
Spread a layer of glue on one of the wide sides of a 12-inch 2 x 8 lower leg.
Lay the lower leg on the side of one of the 19 1/2-inch 2 x 8 long legs. Position them so that both sides and one of the ends are aligned, giving you a single leg with a 7 1/2-inch notch. Clamp them until the glue dries.
Repeat with the remaining leg pieces. When finished, you will have four identical legs.
Build the End Rail Assemblies
Take one of the 40-inch 2 x 8s and one of the 40-inch 2 x 4s. Apply glue to one of the 4-inch sides of the 2 x 4 and attach it to the 2 x 8, aligning one long side and both ends. Clamp the pieces together.
Drill five holes through the 2 x 4 into the 2 x 8, countersinking the holes halfway into the 2 x 4. Drill five holes: The first six inches from one end, the next 13 inches from the end, then 20 inches, 27 inches, and finally 34 inches. Screw the pieces together, using five screws.
Repeat the first two steps with the other 40-inch 2 x 8 and another of the 40-inch 2 x 4s. This completes the end rail assemblies.
Build the Platform Box
Attach one end rail assembly to the end of one 83-inch 2 x 8 side rail; the 2 x 4s on the assembly should face toward the inside of the box. Drill six holes through the side rail into the end rail assembly -- four in a straight line into the 2 x 8 end rail (spaced 1 1/2 inches apart), and two into the 2 x 4 (also 1 1/2 inches apart). Countersink the holes halfway into the side rail, and screw them together using six screws.
Repeat the last step at the other end of the side rail, using the other end rail assembly. Be certain that the 2 x 4 of the end rail faces inside the box, toward the other end rail.
Mount one of the remaining 2 x 4 platform supports to the side rail. Place it at the halfway point of the side rail, and orient it so it matches the 2 x 4s on the end rails. Drill two holes (1 1/2 inches apart) through the side rail into the end of the 2 x 4, countersinking the holes halfway. Screw the side rail and platform support together using two screws.
Position the two remaining platform supports; place one of the supports halfway between the center support and one end rail, and the other support halfway between the center support and the other end rail. Attach them using the same procedure you used to attach the center support.
Follow steps 1 through 4 to attach the remaining side rail to the other end of the supports. This completes the support frame.
Lay the plywood platform inside the support frame. Drill 15 holes through the platform into the support rails -- three holes in each rail, one in the center of the rail and one 6 inches from each end. Screw it together with 15 screws.
Add the Legs and Finish
Spread a layer of glue inside the notch of one of the legs, then fit the notch against the side rail; position it three inches from the end of the platform box.
Drill nine holes through the leg into the side rail. The holes will form a square pattern, 6 x 6 inches, with a nail in the center; the first hole should be one inch from the top of the leg and one inch from the side. Countersink them halfway into the leg.
Screw the leg to the side rail with nine screws.
Repeat these steps with the other three legs.
Fill all screw holes with wood putty. When it dries, sand it smooth with the sandpaper.
Finish as desired, and your twin bed frame is finished.