When you have the Spell book in your hand, press Shift and Right click to
open the spell book interface. By default, the Z and X keys cycle through the available spells in the leftmost column. In addition, one can scroll through the left column
Arcane Spell BookEdit
This is the same as a normal spell book, but it slightly buffs damage and reduces mana cost for all spells stored inside of it. It rarely drops from the Arcane Guardian.
There is a fairly common glitch where you will be unable to scroll through your spells, especially with Z and X, as it automatically crashes your instance of Minecraft. Be wary. This is also an issue with the Arcane Spell Book.