My stories, based loosely on Ojibwa (American Indian) mythology, make use of elemental "medicine" (I shy away from the word "magic," because in this world, it's not considered magic, it's just another form of power). Since the nature spirits are mostly related to natural things, then the medicine is too, though I often categorize it with European elemental terms (earth, air, fire, water and related things like stone, sand, ice, wood, lightning, etc.).
The way medicine is usually obtained is, you're either born with it (meaning you have some supernatural lineage), or you're granted it (permanently, from a patron spirit, or just on an "as needed" basis). Those who don't have medicine but want to use it must "ask" for it from the nature spirits, who may not choose to give it, so it's sometimes unreliable; also, the more one uses medicine, especially without properly asking or thanking for it (or in a manner which the spirits find offensive or harmful), the less likely the spirits are to be generous enough to loan it. Also, thanking a spirit for lending its power is strongly encouraged. The spirits are "people" just like everyone else, after all. They can be influenced, and even coerced, but the latter can be a bad thing (see below).
There are means by which to manipulate people by utilizing some part of their person (similar to the stereotypical voodoo doll), and of course there's lots of emphasis on the power of dreams, written symbols, songs, dances, etc.
There are minor spirits (mostly nature spirits), and major spirits, the latter of whom often choose certain people to become the patron of and grant powers to. Meaning, one person might have a bear spirit as his patron, another person might have the North Wind, etc. The powers a person gets depend heavily on the spirit which favors them. These spirits are "acquired" usually through a dream or vision.
There's also a strong emphasis on equal exchange--you have to pay for what you get, and what you cast out might come back at you eventually (e. g., the more powerful you become and the more easily you can force a spirit to do your bidding, the greater your chances of ending up regretting it)--and if this isn't followed then great imbalance can occur.
That's the magic system I use, at least.
I don't really care for wand waving and funny hats and stuff like that, though I do have people shaking rattles and wearing feathers...