@dushanan have you ever heard of a bard? or perhaps a paladin? just because you use magic doesn't mean you need to read it from a book, magic can be obtained from various sources.
@Dushanan in the story, it's explained she memorized the incantations she heard her adoptive mother use, because she wanted to make her proud.
As for why she's actually able to use magic, she's from a magical family, so it's hereditary.
Nino is.... a good girl.
@Dushanan
That's a direct reference to the Nino/Erk supports in the original game.
Nino doesn't know how to read, she is a natural at magic, though, so she managed to learn by imitating her "mother", Sonia.
Sonia did hate and abused the girl, so never actually attempted at improving her literacy.
As a side note this support was in turn a throwback reference to a bit of Akaneia/Jugdral FE Lore: wizards requires grimoires as magical tools to cast spells without exerting their life force (unlike i.e. Valencia's casters), but aren't actually required to read during combat, they just need to know how to cast the spell and draw power from the magical book.
Each grimoire still has the specific spell written on, until its power is entirely consumed and change back into a blank book, so learning from the grimoire it's the most obvious way to master the spell.
@Bainhardt@DarkKain ah that makes sense. I never did Nino/Erk supports so I missed out on that. And considering her only positive family members were the nonmagical ones I didn't think about her imitating Sonia.
(also yes, Nino is a very good girl)
@MistLynx look, for paladins that's just the power of religion. and bards its the power of music!