There are many sources of information on book binding (one of the best is by Angela Sutton) and this site is not intended to compete with those. Making a book is a series of steps requiring differing skills and, of course, the right tools. This is a very brief description.
Books contain pages, of course. Pages are made up of sheets folded to form a spine, A3 folded for an A4 book, A4 folded for A5 and so forth. These folded sheets are then gathered together, perhaps in fours, with each inserted into the last to give a sort of magazine appearance. There will be many of these gatherings in a book. If, for example, there are twenty gatherings of four sheets the book would have 320 pages or 160 leaves. These gatherings are then sawn or pierced where the thread is to be inserted.
These are just that, cords usually made of a number of thinner cords each of thinner fibres of hemp wound together. These will need to be frayed in the assembly process so a loose twist is desireable.
These are usually made of wood though pasteboard has been used in the past and dense boards made for the purpose are also used today. These are cut to the size of the book and, sometimes rounded at the square edges.
The ideal leather is soft and thin and goat skins are ideal for this purpose. Because this is a natural product there may be blemishes on the skin and marks where the hair once was but these can be incorporated without detracting from the appearance of the finished book.
The tension of the cords is important so a sewing frame (illustrated) is used. This has a base with an adjustable height bar. The cords are secured to the base and the bar and then tightened. With the cords securely held the gatherings can be presented one by and a stitch of waxed linen thread passed through the holes and around the cords moving in alternating directions and securing each gathering to the previous until all are sewn into what is known as the text block.
Because the gatherings consist of folded sheets inserted into each other an uneven edge is created opposite the fold. This is removed using a tub and plough.
The tub is the frame supporting the finishing press, the vice like assembly and, upon this and fitted into a groove in the press is the plough. This consists of a blade held by an adjustable device which allows the blade to be moved by very small amounts. With the text block held in the press the plough is slid across the press with the blade moved further towards the text block at each move. The blade slices the sheets to a nice level edge.
To achieve a rounded and tidy spine the text block is inserted into the press between two thick boards which have an angled edge. The spine of the book is gently rounded by hand and, finally, with a light hammer and then inserted between these boards when the hammer is used to create a recess for the book boards, backing the text block. The spine is lightly pasted to fix it.
The boards are drilled with holes matching the positions of the punched or sewn holes in the text block. The cords which are attached to the text block are passed through the holes from the outside inwards and cut to a shorter length. They are then frayed and spread against what will be the inside of the cover and glued in place.
The leather is carefully cut to size and then pasted over the boards and spine being smoothed over the cords to produce the characteristic raised spine. The edges are mitred, folded and pasted in.
It was the practice in medieval times to tool books with gold or decorate with blind tooling. Blind tooling is a process where metal tools are heated and applied to the dampened leather of the covers. These take the form of single or multiple lines and stamps of various designs.
The dampness of the leather and the heat of the tools have to be carefully managed to achieve a good result and some very complicated designs can be created with stamps and a few tools.