Tbh, it seems like a large amount of mages are born into regular people, but somehow gain their powers. Taliyah was just a random stoneweaver, and now Lux just randomly gained hers. I haven't looked into many others, and I know not all mages find their power this way. Just curious because it seems to be a running theme, and I thought it might spark some kind of discussion.
So it's not known for sure but there is a theory that 
got her powers because she was born so close to Icathia.
Anyways I think a lot of them are normal people that all happen into it by chance or some other force, which makes sense, they are just normal humans after all.
and 
were chosen by aspects of Mount Targon.
Due to his obssession with blood and drive to murder he flees Noxus. He finds a blood mage and learns under him.
Was tortured by Noxians and after sought out dark mages and the like to learn from. He will fix society by bringing it to its knees. (He's a yordle so idk if he technically counts but I like him so he's here)
Was led to the void and then basically consumed by it, becoming its prophet.
Also found the void, his outcome was a little different though.
Finds a gauntlet that lets him channel magic energy.
There are quite a few who are just born inherently magic though. 
for example. Channeling magic through his weapons to turn people into art. Or 
who, as a mixture of her parents and her birthplace, has strong natural magic powers. 
is even a champion who I believe was born with it naturally, it just happened to actually manifest a little later, and then due to living in Demacia she repressed it even more. I could be wrong but I don't think there is an event that gives her magic powers, she always technically was.
As far as i remember, the only ones that actually learned how to use magic are 
... and maybe 
But i could be wrong.
It's a common theme that is primarily used as an allegory for puberty or even "coming out".
I thought Lux gained hers cause she's brighter then my future. It says she can reverse engineer an arcane magic spell just by looking at it.
In general it looks like you'll have to be born with magical abilities in order to use magic(or you have to gain them through some other magical creature/object)
So someone like 
would never be able to cast a spell without the help of someone/something else.
