This is quite a lengthy process: first the cardboard are cut roughly to size.
The special flannel that will be on the inside of the case has to be dyed to match the leather, or one of the design elements of the book, and left to dry thoroughly.
In the meantime, the carton receives its first layer of brown packing paper and it is left to dry in the open. The humidity in the glue causes a reaction in the cardboard and it curls in on itself as the glue dries and pulls the paper tight (that's why we use the packing paper - it's light but tough). Then you wait 24 hours, and repeat the process, so now you have pieces of cardboard that are completely arced. Like this one in the photo, which has been glued in preparation for the last step - gluing the flannel on.
So the end result looks like the photo below.