I'm trying to create a character. I've already worked out some of my character. My character is, at the moment, superstitious with that being pretty much the only personality trait. It has glamours and can change shape. I'm also not planning on following a template. I was hoping to have my character get magic through exposure, I guess, but I'm not quite sure how a character is exposed to magic in a way that would cause the character to be magical. How is a character exposed to magic?
In a game as abstract as FATE, you're actually facilitated fairly well as to how these sorts of things may happen. If you can feed a pretense into the plot device, and your GM is okay with the change, the rest become plot bait and you crank the device. Popular examples involve rare (nay unheard of) rituals good for just one more use, untapped latent power, finding a place of power, finding a being willing to "Sponsor" you and have the actual magic develop on its own over IC time, and my personal favorite: the body swap where the minds change but not the powers.
Your patience is entirely critical, because most of the time you won't just simply become a full blown Wizard overnight. You may have to do some fledgeling work, then Sorcerer, Conjurer, and finally get chest deep. A sudden change requires a mega burst of DM Magic and heads turning the other way even in the buttery soft sci-fi world that is Dresden.
A lot is going to depend on what you mean by 'get magic'. A lot of it is going to depend on your GM, so that would be a good first place to start, i.e. talking with him about what you're trying to do. Moving on to the character, there are two sides to this, but after the comment above, I'll start with systematically.
In DFRPG, you have to justify supernatural powers with, at the least, an appropriate High Concept (see
The larger issue (and the reason I stated that you should talk to the GM) is the in-game rationale, especially if you're planning to do this during play. It is going to depend a lot on your GM's interpretation, as such an event isn't really covered in the books as written. Find out before you get too deep into the concept what your GM will allow, as that's going to be the framework for if this is possible, and under what circumstances it would be possible.