Remove the book block, or pages from the interior of your book, so you can see the entire spine. Insert the plastic strip so it's lying against the inside of the spine, between the front and back covers.
Rub sandpaper gently along the spine to remove some of the excess adhesive not covered by the strip of plastic. Remove just enough to ensure a better bond, but leave some of the old adhesive behind so your newer layer of PVA adhesive has something to hold on to.
Put PVA adhesive in a small glass bowl or dish. Mix in a few drops of water so the adhesive runs smoothly, but not to the point of it being too watery or hard to control. Brush a very thin layer onto the spine. This will becoming the bonding layer between the old and new adhesive.
Use some of the PVA adhesive to glue down the worn edge of your book block. Your book block may not need repairing. However, if a segment of the outer edge has curled up, glue it back down, using a screwdriver to press down the curled edge. Make sure not to get any adhesive inside the book itself, on any of the lettering. It's important that the curled or loose paper stays down on its own once glued.
Brush a good amount of adhesive into the spine of the book where you inserted the plastic strip. This layer of glue will bond the binding and book block together in the next step. Wait for the book binding to soak up some of the adhesive before continuing.
Place the book block along the spine, aligning it so both back hinges of the book look correct. Reposition the book block if necessary as the adhesive won't begin to dry for a few minutes.
Place wax paper between the book block and the front and back covers of the book. Make sure the wax paper's inserted into the hinge. This will help prevent excess adhesive gluing the covers of the book to the interior itself.
Close the book and set one dowel rod on each cover joint. Sandwich the book between two, flat boards with the dowels still in place. Wait 24 hours before moving on to the next step.
Remove the boards and rods before opening the book. Look at where the inside of your covers meet the interior of your book. You might notice the endpapers, or the paper glued against the inside of each cover, aren't attached to the rest of the book.
Use your X-Acto knife to cut away some of the excess paper, and then use more of the PVA adhesive to glue the edge of your book's endpaper to the interior book block. Do this for both the front and back covers. Wait for one to dry before starting on the other.
Close the book, add the dowel rods like you did before on the front and back covers and then compress the book for 24 hours by placing it between two flat boards.