If you want to be any good at magic, you'll need to gather Mana from your God, which will enable you, for instance, to research spells. Each of your cities can hold up to 4 religious buildings that are dedicated to your God. This will please him and through them you'll be able to gain more and more Mana as this capacity increases. Of course, the higher the building's level, the greater the Mana capacity. Similarly, your God's satisfaction increases as you spread his word through the other races and realms of Akeran, and so does your Mana capacity.
Then, each New Moon, your God will reward you with a quantity of Mana that depends on your Mana Capacity, but also, more importantly, on your Grace. The higher your Grace, the faster you'll replenish your Mana Pool up to your maximum Capacity. However, if your Grace is low, your God probably won't award you much, and he might even take some back if your Grace is too low. Hence, if you plan to do some Magic, better not anger your God.
As soon as your first magic building has been erected, you can begin to research spells. There are 7 realms of magic belonging to either God Magic (Briac, Khorg) or Elementary Magic (Draconians, Dwarves, Elves, Humans, or Nomads). According to your allegiance, one domain of God Magic is accessible to you. Likely, the Elementary Magic of a race can be researched in every town of the same race where religious building exists. Once you have completed the research of a spell, you will never forget it.
It is not possible to research in more than one field at the same time. Mail notification is available for reasearch completion. Check your account options.
Completing research implies allocating Mana from your Mana Pool to the current research. You usually choose the amount that shall be spent automatically each New Moon, but can also commit additional Mana whenever you want.
The Magical Advisor lets you check among others the advancement of the current research. Of course, more powerful spells will take longer to research and will need more Mana. This advisor gives you two percentages of completion: One said "optimistic", and ... the other one. You have a chance to succeed (i.e. complete your research) as soon as the optimistic percentage reaches 100%. In any case, the research will be over when the pessimistic one does.
Once you have discovered a spell, you can make your wisdom available to some of your places. To achieve that, you need to cast a ritual that will establish a link between you and the religious buildings in your city. Establishing rituals costs Mana, and so does maintaining established ones. You'll soon discover that managing your Mana is no easy task, and you'll have to make choices between rituals and researches. If you run out of Mana, some rituals may even get interrupted, and you will probably need to establish them anew.
When you have established a ritual in a city, your spellcasting units can learn it. Indeed, each of the magical building discussed above allows you to train specific spellcasting units (or "magical" units). Spellcasters all have a magical ability, and more importantly an elementary Mana pool. Both depend on the unit's level, and its magical experience. Spellcasters regain Elementary Mana every moon, if they are resting, and in greater amount if located in their home realm. Moreover, if a spellcaster is in a city of its race, it will gain a lot more Mana, depending on the magical buildings in this city, its population, and your God's consideration. Spellcasters cannot regain more than 10% of their mana pool in a single moon.
You can improve a magical unit's spellcasting ability and increase it's Mana pool by making it study the magical arts in a suitably complex building (if the building's level is too low, the unit won't learn anything).
As said above, in a given city, spellcasting units can learn spells which rituals have been established. Low level units may have trouble learning higher levels of spells, it stands to reason. However, once a unit has managed to learn a spell, it'll know it untill it dies (regardless of the ritual being severed or anything).
Any known spell can be cast by the unit. Some spells will have an immediate effect, whereas most will simply enchant a target unit (spellcaster, fighter, or non-fighting unit), and be triggered by any event corresponding to the spell's instructions (usually, it'll be a fight, or a movement). Have a look at the Spell Book for a more detailed description.