Lay two 1-by-24-by-36-inch plywood boards on the working surface, evenly set on top of each other. Draw a line from one corner of the board diagonally across to the other corner. Mark a position eight inches up the line from what will be the bottom corner of the line. Mark another position three inches further up. Continue to mark positions every three inches until you get to the top corner of the line. Go back and mark another position one inch directly below each marking, excluding the first and last markings along the diagonal line.
Drill a hole in each marked position, extending the hole all the way through both boards. Stand the two boards upright and have an assistant hold them in place on their short, thin sides. Spread the boards about two feet apart with the holes mirroring each other.
Set a 1/2-inch wide, 24-inch long dowel in each pair of holes, positioned evenly between the two side boards.
Fold over 1/4-inch of each edge of a 18-by-22-inch piece of fabric. Sew the seam along the folded over section to hem each edge. Fold over one edge of the fabric to make a 1-inch overlap. Sew along what was the edge to make this into a 1-inch pocket. Repeat for the opposite side of the fabric.
Slide one of the side boards of the bookcase off. Have an assistant hold the remaining side board and the dowels upright. Slide one of the fabric pockets over the bottom dowel. Slide the other fabric pocket of the fabric section over the adjoining dowel, putting it on the upper dowel rather than the lower one at that position.
Create another fabric section with the two pockets and attach it to the open dowel directly below the top end of the already-attached fabric section. Slide the other end of this new fabric to the adjoining upper dowel. Repeat to attach fabric sections to the entire bookcase, creating fabric shelves for the books to rest in.