Measure the width of the wall that will support your built-in bookcase with a measuring tape.
Cut two 2-inch-by-4-inch pressure-treated lumber sections to the width of the wall with a circular saw. These sections will serve as the top and bottom plates of the wall.
Lay the bottom plate along the floor between the adjoining walls. Use a carpenter's square to make sure the plate rests at a 90-degree angle to both adjoining walls. Drive 4-inch wood screws through the bottom plate into the subfloor at 4-inch intervals with an electric screwdriver.
Position and install the top plate parallel to the bottom plate and check the position with a carpenter's square. Attach the top plate to the ceiling with 4-inch wood screws at 4-inch intervals.
Measure the vertical distance between the top and bottom plates. Cut sections of 2-inch-by-4-inch pressure-treated lumber to this length to form the studs. You will need one stud for each side of the wall, plus one stud for each 16 inches of wall length.
Place one stud between the top and bottom wall plates against both adjoining walls. Check the studs with a carpenter's level to make sure the studs are perfectly vertical. Secure these studs to the adjoining wall studs with 4-inch wood screws.
Mark the top and bottom plates with a pencil at 16-inch intervals. Center one of the remaining studs on each mark, and check each stud with a carpenter's level. Insert 4-inch wood screws through the stud sides into the top and bottom plates at 45-degree angles.
Cut 3/8-inch plywood sheets with a table saw to fit the wall. Position the plywood sheets against the wall and secure them to each stud with 4-inch wood screws at 4-inch intervals.