The "S" key on my keyboard is currently broken and needs to be tapped more than once at the moment, o if there a typo that' probably why.
If magic is something anyone can do, it should be taught even in all schools. It'll probably look a lot like chemistry class, honestly, just with chemical reactions swapped with spells. Heck, magic may even be fused with the natural sciences and taught as a part of that curriculum. Even if not everyone can perform magic, there will probably be some courses on "this is what happens when a mage does this, this is what they can do, this is what they can't do, this is why" in all schools, whether there's a scientific explanation or it's simply up to the whims of the gods – unless, of course, it's a segregated society like in Harry Potter.
Other than that? That depends on educational ideology. Some educational institutions may teach practical skills, like carpentry, plumbing, how to repair a broken pentacle and reenchant an amulet, working with cars, etc..
Some educational institutions will focus more on liberal arts, where things may be a little bit different. At first, history will just be history, but later things will get specific: "world history," "economic history," "magical history," "religious history," "[insert country here]ian history".
There will also probably be math and physics and such. Harry Potter didn't do this, which I think is silly. Even if magic and technology utterly fail to work together, you're still going to have wizard economists and wizard business owners who are going to want to understand math, and wizards who want to blow things up who need to know if the blast from this spell or another will be enough to destroy a building.
There may be specific classes dedicated to studying different types of magic, but honestly unless there's a very specific, concrete difference between the "schools of magic" and the way they're done I don't see any practical reason to separate them. In Harry Potter, you have "hexes" and "jinxes" and "transfigurations," but transfiguring someone into a rock is a perfectly good way to kill them, so what's the point? I still stand by my assertion that magic would probably be taught alongside the natural sciences, possibly with some classes having more emphasis on the magical parts than others.
It should probably look like a normal school for the most part, with magic being integrated into the math and science portions. You may think "but then only the nerds will want to do magic!" Exactly. In real life, we can break free of the atmosphere and turn lead into gold and make electricity sing, yet we still look to fantasy for the fantastic. I mean, we made green fire that looks like something out of Harry Potter in chemistry and no one considered it terribly awesome. Kids in your world, who are constantly exposed to magic, will see it as something normal… and probably as something nerdy.