There are two types of spells.
Healing spells will raise your skills (Health, Fatigue, Strength, Mind, Luck). To use a healing spell, add it to your inventory and click on it. Clicking on the spell will cast it on yourself.
Damage spells can only be used against monsters. When you attack a monster, the fight will automatically pick the first weapon in your inventory (from left to right). Your spell will be used the same as any other weapon.
To change weapons during battle, click on another weapon/spell to jump it to the front of your inventory.