Measure the available space to determine the size of the curved bookcase. Sketch the bookcase on graph paper and use a scale of one square for every 6 inches to obtain a visual reference to use while cutting and building.
Draw the curve of the front of the bookcase on a large sheet of cardboard or thick paper. Draw a second curve for the back of the bookcase. Check the distance between the curves with a ruler to make sure the depth of the bookcase will be consistent along its width -- most bookshelves are at least 12 inches deep.
Cut the cardboard or thick paper along the curves with a utility knife to form a template for marking and cutting the bottom plate, top plate and shelves. Transfer the width of the bookcase to the template and cut straight lines with a metal straightedge as a guide, from front to back on each side to finish the template.
Place the template on top of a 1-inch-thick section of pine or hardwood large enough to accommodate the entire template. Draw along the curves then remove the template and cut along the curves with a bandsaw to form the bottom plate. Repeat this process with additional sections of pine or hardwood to form the top plate and shelves of the bookcase.
Measure and mark two sections of 1-inch-thick pine or hardwood to the height and depth of the bookcase. Cut these sections to size with a table saw to form the sides of the bookcase.
Place the bottom plate on the floor and stand one of the sides at each end. Insert 2-inch wood screws through the sides into the ends of the bottom plate at 2-inch intervals with a drill and a screw bit.
Ask a helper to hold the top plate between the sides and flush with the top edges of the sides. Insert and tighten 2-inch wood screws through the sides into the ends of the top plate at 2-inch intervals. Repeat this process with the shelves and check each shelf with a carpenter's level to ensure it is level.
Measure the width of the bookcase along the back edge. Transfer this measurement and the height measurement to a 4-by-8 foot sheet of 1/4-inch-thick plywood. Cut the plywood sheet to size with the table saw.
Place the plywood sheet on the back of the bookcase and align the edges. Insert and tighten 2-inch wood screws through the plywood into the bookcase at 2-inch intervals along the perimeter.
Fill in the visible screw heads with wood putty and a 1/2-inch putty knife. Sand the surfaces with a palm sander then stain or paint the wood to give the bookcase a finished look.