These are very useful, especially when pasting. They can be improvised in numerous ways.
I shall write a separate note on specialist pressing boards ~ which have a brass strip attached. They are of limited use for the general pressing discussed here.The essential properties of a pressing board are that it be completely flat and unwarped. Next ~ it must remain so in use ~ which may men being dampened. Natural wood absorbs moisture and is prone to warp as it dries. Well seasoned wood is less likely to warp, but is also a rare commodity these days. Most modern timbers are kiln dried and that means they are seasoned enough for general uses. In days of old ~ a century ago ~ timber was rough sawn and then stacked in piles which allowed air to circulate. These piles were left outside but under cover for several years. Once dry sealing with varnish or some other chemical is useful, but not always a guarantee. Oil-based seals must be avoided at all costs.
For many years birch plywood has been made, and is widely available in several qualities. The best quality is unlikely to warp. It is made in a variety of thicknesses and is recommended ~ if you can get hold of it ~ at a suitable size ~ at reasonable cost. It can be more expensive that it needs to be. Shop around ~ and avoid cheap substitutes. (How? I do not know ~ other than through sad experience.) More on this later.
If your workbench is cluttered then you will need to move the drying materials to a separate surface. It is convenient therefor to use one drying board as a base and another as a top. If the boards are thick enough then for a pile of books one board per book and one to spare is sufficient.