Cut two rectangles of a sturdy cotton fabric, each 45 inches wide and 81 inches long. This allows for a twin futon about 5 inches thick. Cut larger rectangles if you want a thicker futon.
Construct the futon cover. Sew the two rectangles together on three sides, leaving the fourth side open. Use a 1/2-inch seam allowance to ensure a sturdy seam. Turn the cover inside out.
Create the mattress structure. Cut a piece of foam into a rectangle 39 inches wide and 75 inches long. Wrap the rectangle in cotton or wool batting. You can stack multiple thin pieces of foam or use more than one layer of batting to build the mattress up to the desired thickness. If the stacked foam tends to slide, spray it with foam adhesive to create a non-shifting block.
Slide the sandwich of batting and foam into the futon cover, making sure that the futon structure fits all the way into the corners of the cover.
Pull the open edges of the futon cover closed over the foam. Sew them together using a blind stitch or whip stitch, tucking the raw edges inside.