Buy or order conventional torsion springs. Purchase pre-cut slats of wood, wood screws, L-brackets and other needed items beforehand.
Place the wood slats in order according to size close to the work area. Separate all screws and brackets into a bowl or bucket. Have a screwdriver (electric is preferred) close at hand along with the wood glue.
Lay the two 38.6(L)-by-7(H)-by-2(W)-inch wood slats and two of the 17.3(L)-by-7(H)-by-2(W)-inch wood slats flat on the table then drill four holes in each slat of wood on each end, two of them 1 inch from the top and two 1 inch from the bottom. Then drill one whole in each end of the 17.3(L)-by-3.5(H)-by-1(W)-inch wood slat.
Take one of the 38.6(L)-by-7(H)-by-2(W)-inch wood slats and one of the 17.3(L)-by-7(H)-by-2(W)-inch wood slats, bringing them together on one end and making an L shape that is 38.6 inches in length and 7 inches in height. Attach the slats of wood using two L-brackets and two #10-by-1-1/4-inch wood screws, fill 1/3 of each hole with wood glue before inserting the screw, then repeat the same process for each corner of the frame. Allow the wood to dry. You will end up with a box-shaped frame.
Halfway between the long length of the box, lay the 17.3(L)-by-3.5(H) flat going across from one side of the frame to the other; attach the wood to the frame using two #5-by-5/8-inch wood screws. Then attach the 17.2-by-1-inch thin wood slats using the other #5-by-5/8-inch wood screws, placing them 6.9 inches from each other with four on each side of the 17.3(L)-by-3.5(H) center piece.
Lay the vinyl box spring encasings across the frame and down the sides, then carefully turn the box over and lay the conventional torsion springs inside of the box. Using the brackets and screws that came with the springs, attach it to the frame. Zip the vinyl box spring encasings starting on each end working towards the other end. Wipe the vinyl down with wet cloths and move to where you want the new box spring.