Sand the parts for the single bed base: four planks of 2-by-12 lumber cut to 39 inches and two planks cut to 76 inches.
Paint all the components for the platform bed, the base pieces plus two planks of 1-inch-thick MDF cut to 25 by 80 inches. Paint on a couple of coats in the desired color and leave to dry for the time recommended on the paint can label.
Position the four 39-inch-long planks on a 2-inch edge and 19 inches apart; they should be parallel with each other in a row.
Abut the two 76-inch planks with the ends of the 39-inch planks, so that the outer two short planks form corners with the ends of the long planks.
Square off the 39-inch planks with a carpenter's square so that their ends are at right angles to the 76-inch planks and clamp them in position.
Drive 3-inch wood screws every 4 inches through the sides of the 76-inch planks into the ends of each 39-inch plank to hold the bed base together. Remove the clamps and retouch the long planks with paint to obscure the screw heads.
Center the two MDF sheets, stacked, on top of the base, with the 80-inch sides parallel to the 76-inch sides of the base. There should be roughly 5 inches of overlap on each side of the base, and around half that on both ends.
Secure the MDF sheets to the base with wood screws driven every 10 inches around the perimeter of the platform into the base underneath.