Cut the 2-by-6s for the frames for your walls. You will need two pieces that are the length of the wall you are building. These pieces are the top and bottom of the frame. The stud pieces will be the height from floor to ceiling, less 4 inches. You will need enough studs to put one on each end of the frame and every 6 inches across the length of the wall. Cut the plywood for the shelves. You will need a piece that is 16 inches by the height of your studs for the back, and two pieces that are 5-1/2 inches by the height of the studs for the sides of the shelves. The shelves themselves should be 15-by-5 1/2 inches.
Build the wall frame. Lay out the top and bottom pieces and two of the studs to make a square. Nail them together so that the 6-inch side will lie flat against the ceiling and the wall. Use two nails per side for each stud and nail them into place. Make sure the corners are square then nail the studs into place every 16 inches across the length of the wall. Put the wall frame up by nailing it to the corners of the other framed walls. Nail the wall frame into the floor and ceiling joists on either side of each stud.
Use a pegboard as a guide to drill 1/2-inch-deep holes at the 2- and 4-inch marks on the side pieces for the shelves. These pieces determine the height of the studs by 5-1/2 inches. Drill the holes every 2 inches down from top to bottom. These will allow you to change the height of your shelves as needed. Sand and paint the front and the back pieces of the built-in shelves.
Nail the sides of the shelves to the back of the shelf. Do this for each built-in shelving unit you are building. Then slide the back piece of the shelving unit into the installation area. Nail or screw this into place on either side of the 2-by-6 inch stud it fits between.
Hang the drywall along the rest of the wall. Use drywall screws into each stud at the top, bottom and middle of each piece of drywall. Cover the seams with drywall tape and compound and cover the screws with compound as well. Allow the compound to dry then sand the drywall smooth and paint the walls.
Install trim along the edges of the built-in bookshelves for a finished look. Then install baseboards along the bottom of the wall. Mount the peg shelf holders in place at the height you want the shelves then install the shelves on top.