Your party will know some spells, and not know others. ‘knowing’ does not mean you are proficient in them in any way (yet). The party will know some basic spells from the start, because everyone has heard of them or seen them in practice. Again, this does not mean everyone can cast them.  If you find a spell book of a previously unknown spell, the spell becomes known to the party. Known means the picture and description will appear if you select it in its spell group in the ABILITIES -> SPELLS section

If you know a spell, and a player has talent points to spare, in theory he can spend one to improve his spell proficiency in that spell, assuming:
a) his class cap for that spell isn’t already exceed by him. A cleric can learn the spell magic missile, but he will never be really good at it. Just not his cup of tea.
b) his spell proficiency has not already reached or exceeded his magic lore skill. to STUDY a spell via talent points means to improve what you are doing, and that requires knowledge about how the fabric of magic and this particular spell works. Most spell casters can be trained in this, but some better than others. Studying magic extensively is the speciality of wizards and geomancer and to some extent priests.

If your proficiency is at least 1, you can cast a spell. All spells are displaying their ‘level’ in roman numbers. Simply to visually get an indication how powerful you are casting the spell. Roman I means proficiency of 1-9, II means 10-19, VI means 50-59 and so on.

When you cast spells, you will eventually get better at them. How fast / how many practices it takes is different for each spell and I won’t reveal the exact figures. I don’t want spells like magic missile that work on auto to go up in proficiency every other fight. That would make it too powerful too quickly.

The class max limit does NOT apply for learning by doing, you can always become a FREAK in your class by doing things others in your class don’t normally do. I am yet looking forward to someone dedicating some time building a druid with a “divine widow maker of shock” (a ranged weapon) with a ranged weapon skill of 99, casting HASTE at spell level 10 and basically knocking an army of golems out of the park in a matter of seconds. Possible, yet quite a task to complete …

NPCs can also sometimes give you knowledge (and sometimes starting proficiency of 1) in a spell. I think holy smite and holy plasma gets awarded by an NPC from memory.

On class change, all classes gain a few proficiency points in either new, or existing skills or spells that the new class is specifically good with.

SPELL BOOKS help magic users boost their spell proficiency through ‘study'(use of talent points). They can study regardless, but with books it yields bigger proficiency increases. You are capped though in this method by your magic lore skill.
Books can be seen for each spell individually in the spell’s details when looking at ABILITIES -> SPELLS.

If you find a spellbook, it has a ‘rank’ which is represented by its name.  “Basics of” is a low rank.  “Tome of” is a higher one.  When you find one you already have, it is worthless.  However the game checks if there is a lower level one you don’t already have and changes it to that if the case.  Having a high rank and low rank book is better than just having the high rank one.

Common places to find spellbooks are: when defeating a spellcaster like an orc mage (low chance) or a beholder (high chance) or a conjurer ; when looting the top level of the lich tower (several are found there); when finding rare hideouts of spellcasters (there is one hidden away deep in the watery caves when you follow the river up into the mountain, just west of the starting shelter. If a spell is generally known, but your proficiency is zero, then you can learn it as well by spending talent points. For example if you have a druid and a mage in your party, they can effectively learn each other’s spells this way.