Even wizards who can do magic with will power, not spells, can benefit from training. One element that distinguishes mankind (at least on Earth) is the ability to learn from predecessors. And wizards are likely the elite, having more specialized knowledge that can be passed down. While some of that can be done via books or scrolls, personal interaction tends to be superior to written material. To determine how much training is available and what form it likely takes, we should determine the prevalence of magic as previously discussed.
At its rarest, magic will only be taught by individual wizards in a master/apprentice scenario. At its most common, there are wizardry schools, possibly many of them held in differing esteem, and with and practices. Aside from prevalence, the other major factor determining this is public and government attitudes toward magic. Naturally, where it’s forbidden, the secret apprenticeship is more likely, but where it is openly accepted and plenty of wizards are around, a school may exist.
We can use this to develop character backstory. If they have little to no training, that will explain some mishaps and inconsistency. They may even be able to do some spells without all of the words, gestures, or ingredients, somehow compensating for it. Someone who goes to a prestigious wizardry school will be known for that. Those who had a secret internship, possibly with someone disreputable, may keep quiet about it and refuse to admit to their master’s whereabouts. Every wizard is likely to have an accident of some kind in their past, and training certainly influences the number and severity of these, plus the emotional and even physical scars that result. A wizard without fear is a fool.
To create a school of magic and its curriculum or books, we can leverage subjects from our own schooling. What typically exists? Potions, summoning, communication, creating and using items, material usage (plants, animals, etc.), history, school of magic, types of magic, general spell casting 101, and more. Unless we’re planning to have a character in a Harry Potter-like setting, we don’t need too many details, but it’s worth inventing this once and having it in mind for most of our fantasy worlds because much of it would exist on all of them, even if the class or book titles change. Inventing a magic curriculum can be fun.
Determine how long school lasts in hours per day, months, and years and if there are ranks that people achieve at various stages. This can help break “wizards” from one organized mass into smaller groups distinguished from each other. An obvious decision is for multiple years, and with this chosen, we can choose ranks. For example, if it’s seven years, we can use the seven colors in the spectrum to denote those at each stage of completion, and maybe they wear robes of a given color to show it. If it’s four, maybe we use seasons or elements.
Are there tests that must be passed to advance? It seems obvious. We don’t have to decide what they are, but it can add interest, particularly if each year has one test that is more feared than the predecessors. It’s a chance to invent stories about what happened to one person or another when failing. We shouldn’t go too far with this sort of thing unless our story is to heavily feature it.
At what point do graduates become eligible to teach others, whether at school or in an apprenticeship? Why would someone want my teaching instead of yours? Expertise and prestige are two reasons. We can gain the latter due to pedigree, training, accomplishments, and fame. Or even having past students of a given instructor go on to achieve greatness. Invent a famous instructor in the setting and determine why this is so.
We should also determine what happens if someone fails training or is expelled. Are they literally marked in some way, like a thief with a notch in their ear? Or perhaps their abilities have been removed. These people will be around and it makes our setting more believable that one should be encountered, particularly in longer tales. Their fate should be a warning to those in training.