Once we have magic established in a setting, how does one learn to use it?
Good question, and on upon which there has been a ton of ink spilled.
Our historical examples provide a variety of options that are expanded with modern fiction. Over all, they appear, I think, to mimic or mirror contemporary views of general education for the most part.
Lone tutelage was commonly expressed in ancient and medieval sources. The case of the master-apprentice relationship that runs from Chiron and <insert Greek hero> through Merlin and Nimue of the Arthurian legends. In this set up, either the apprentice seeks out the master who is hidden somewhere, often a hermit, or the master seeks out the apprentice, often secretly watching while in disguise as the apprentice grows. In more recent form, this is played out in the original Star Wars trilogy as Kenobi effectively watches over Luke before revealing Luke’s magical lineage, then Luke seeks out the hermit master (Yoda) to continue his training.
Throughout the early modern period, aka the Renaissance, many held the belief that magic was learned through paranormal tutelage. Referencing Jean Bodin, Kramer & Sprenger (Malleus Maleficarum), and most of the other witch and werewolf hunting sources of the 15th through 19th centuries, magic was learned at the feet of the Devil, or one of Lucifer’s demons. Some other sources speak of genii (of Roman origin; akin to the genius loci) or spirits of the dead visible solely to the magician who provide instruction. These figures sometimes also act as familiars.
In some of the early modern sources, the paranormal tutor introduces the prospective magician to a coven of other magicians, usually witches. This becomes a form of the secret society. Magic instruction via secret society is, I think, a relatively modern idea beginning around the 15th or 16th centuries. More famously, it continues into the semi-secret occult societies of the 18th and 19th centuries including the Hermetic Order of the Golden Dawn (1888) and a host of others. Magical instruction is generally tied to advancement within the mysteries of the society in these situations (this works well with certain RPG systems that use level-based spell casting, like D&D).
Both the RPG industry, some novels, and some historical sources do incorporate religious based magical instruction. One that comes to mind in particular is Katherine Kurtz’s Deryni series in which magic instruction is tied to status within a religious organization (if I recall correctly). This, I think, comes out of the old medieval schools that taught theology, law, medicine, philosophy, history, languages, but were the province of the Church. The only way to receive a certain level of education was to become, on paper at least, a cleric of the Church in Rome. Often, these students wouldn’t become full priests or monks, but would hold a lesser standing in the Church.
Finally, we have schools of magic, which seem to be a modern invention. There may, arguably, be an exception with the stories of Scholomance—a school of dark magic in Eastern Europe. However, the majority come from modern fiction, whether Rowling’s Hogwarts or Charmed’s imaginatively named Magic School. Obviously, the school set up has become popular among children’s and YA authors to connect with their readership. It is even fairly common in adult fiction, from Ilona Andrews (Kate Daniels series) & Devon Monk (Allie Beckstrom series) to Jodi Lyn Nye (Applied Mythology) as well as video games (Wizard 101, Warcraft), comics, and other genres.