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It probably depends on the protagonists. Are they themselves magic users? Or even magic researchers? Is there actually a separate magic research (like the science research system in our world), or ...
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Source: https://writers.stackexchange.com/a/35649 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
It probably depends on the protagonists. Are they themselves magic users? Or even magic researchers? Is there actually a separate magic research (like the science research system in our world), or is magic research something that is done in magic guilds or magic schools that guard their knowledge from competing guilds/schools? All that affects how your protagonists would learn about new magic (and in most cases you'd want them to learn about it before it becomes a story changing element). If they are not magic users themselves, they can learn about it e.g. from rumors ("have you heard, they say that in the evil empire Adolfia, they developed new magic that lets big things fly through air at very high speed; they call it rocket magic") or from travellers ("I've been in Wizard City last week, and I've attended a demonstration of the Great Mage where he showed of his new fire ray magic."), or they may actually witness some new development themselves ("As Tom travelled towards Sometown, he passed a field where a sorcerer did his experiments. Trees were growing out of the ground and reaching full size within minutes. Tom had never before heard about that type of magic; it was common knowledge that magic only could manipulate inanimate objects. But that sorcerer apparently found a way to circumvent this rule."). If the protagonist is a wizard himself, but not a researching one, he might actively seek out other wizards to learn from them ("John looked forward to visiting Nocastle, as it was the home town of William Wandman, a wizard that was known to always be well-informed about new developments in magic. John hoped that he could learn some new spells from him.") Or maybe there are shops selling the newest magic ("The shopkeeper offered him a strange green liquid: 'That's the newest development in magic potions. It allows you to increase your eye's resolution twenty-fold. Just fifty grains for you, a real bargain.'"). If the protagonist is a magic researcher himself, it's of course the easiest: You can just describe how he performs his newest magic experiment. Or maybe he's visiting a wizardry conference, learning about the newest developments.