i go to the local mage guild and ask them to teach me some more.
but there will probably be a fee, so i work until i have 100 gold or whatever.
"Local" would probably mean a 6 day journey or so, for a small place taught by one person when they have spare time or need money. would probably take closer to 10 days to get to a city(and there it would be a small branch of a major guild, so likely "merely" 20 members or so). maybe a month to reach a major city with hundreds of people in a guild, and for the places with thousands, you could only find those in the ~5 largest cities.
Not to discourage you, it's just that if they built a whole school at each town, within a few years they would run out of students and funds, and development of new magic would be *slower* because they would be dispersed across the known world.
Still, if you want to trek out to someone who knows something, you could become an aprentice and get good bonuses until you come close to their level, and if you wanted, you could help them progress further, as group research gets a bonus(Exception: discovery of concepts with no feedback. No matter how many people collaberate, with no way to tell when they are succeeding, the only bonus is that once one succeeds, the rest will get a slight bonus)
Also, smaller locations would have lower fees, to a point. A lone old mage might be happy to teach in return for assistance with physical tasks, but if you decide to go somewhere large enough they will ask for a fee, more famous places would demand larger fees. The point is that the smaller places need the funding, and the larger places need to filter out the less effective students, as they can't afford the time to teach every single person who walks in asking for education.