All right, here are the ancient secrets that are the seeds of wizardry. Pay attention and try not to have any stray thoughts, mortals are not really designed to tinker with the inner workings of the Cosmos.
"Wizardry" is, fundamentally, the weaponisation of thought, awareness, soul. Ever heard a song that made you cry? Made someone do something by choosing the right words? Said the right thing to get out of trouble? Wizardry is basically the same principle. There are words, phrases, lines, ideas that have mystic consequence: a Spell is, in a sense, a kind of spirit, a fragment of sentience, bound and shaped, and "preparing" a Spell means making your own mind into a vessel that can hold it. Get good enough at that, and you can do simple magical workings all by yourself. There are rules, some of them mathematically precise, but they're more like the rules for composing a symphony. Magic is alive.
More simply: magic means visualising the unimaginable, feeling transcendent thoughts, perfectly, without getting lost in them.
Canonical Wizardry is the set of traditional arts taught here, codified by ancient archmages to be relatively safe. Relatively.
Since you're already a wizard of a sort, we can skip the usual initiations and riddles! You already know what Conjuration is; there's also Abjuration, creating shields and protections; Transmutation, altering worldly qualities; Evocation, controlling the elements; Divination, seeing the unseen; Illusion, creating images - oh, Dr Baika already has that one, sorry - and Enchantment, affecting the minds of others. Conjuration, Divination and Enchantment are the most dangerous, in that order. Any of those speak to her?