My toddler daughter loves books but she's still working on how to take care of them. Like most little ones will do at some point, the other night she dismantled her favorite book. Luckily I got to it before she really pulled it apart and managed to find the cardboard spine avoiding the need to make a new one.
It isn't rocket science and I'll be up front in saying that this project is probably more about using the right(purpose made) materials than any clever technique.
Step 1: The stuff
You can repair books with gaffer's tape, packing tape, white glue and denim, whatever but if you want your repair to look like a "book" you'll need book binding cloth and PVA glue.
You can order those online or find them at most any scrap-booking store.
The PVA glue is designed to bond paper like no other glue I have ever encountered and book binders cloth is designed to take a lot of abuse from handling and bending as well as having a paper backing that lends itself to working with PVA.
You'll also need a broken book to repair. I'll leave that up to you.
Step 2: Measure and cut
The only thing to remember is that since the book will bend in a coupe places you need to account for this when you measure and cut your cloth.
You'll also want to leave just a little extra to fold over for a more finished look. Little ones won't much care about this "now" but maybe if their favorite book survives into their adulthood they'll be touched by the loving care that went into saving their cherished reading material.
So, with the book closed wrap a tape measure around the edge to see how wide your book cloth will need to be. Then measure the length of the book and add and inch to give yourself a half inch or so to fold over on either end. This ended up being close to 12 x 6 for my project.
I used scissors but you could use anything that will give you a clean line. Be sure to play attention to the grain of the cloth as it is readily noticeable if it's off even a little.
Step 3: Glue in the spine
I chose to glue the spine to the book binders cloth first. This could have been done differently. The only critical thing to remember is to not glue the spine to the book itself. It needs to move as part of the cover and hinge rather than be affixed to the pages.
You'll also want to make a couple small cuts so you have tabs the width of the spine to fold over and glue to the spine itself. This allows for a clean fold and nicer edge on the cover as well as the spine. Easier to see in the images if you just follow those.
Step 4: Repair the binding
After attaching the spine simply line up the cloth and glue first one side and then the other to the cover. You might want to use a bone burnisher to smooth things out but it isn't really necessary on such a simple repair.
I wrapped my cloth fairly snug to help hold the book together. PVA dries very quickly so be as precise as possible when gluing it down. You likely won't get a second chance.
Step 5: Back in business
Return the beloved book back to your child's library and see them smile.
My little girl was very happy to have her book back. She'd been looking for it for a couple days while I was mending it.