"Hm. There are numerous examples, real and fictional, that we could base our systems off of in my memory.
The first that comes to mind is that magic is essentially a field that permeates the entire universe. Its energy can be leveraged to violate the normal laws of physics, either through a combination of inborn ability and willpower, or careful study of its eddies and flows. Casting more than the most basic spells is fatiguing to the mind and body, and high level spells would exhaust the user. Additionally, magic is divided into several schools based on how it influences the world, including but not limited to evocation, abjuration, illusion, and necromancy.
The second is a bit more interesting and flexible. Magic is sourced from one, infinite source of power that some individuals are born with a connection to. It is filtered into five elements; Earth, Water, Air, Fire, and Spirit, and threads of these are woven together to produce the desired effect. Every weave has the same result every time it is performed correctly, though certain actions - such as unraveling an existing one - can be quite chaotic indeed. One may be born with the innate ability to channel this power and will do so regardless of teaching, born with the ability to learn, or insensitive to it, and each person has a different raw capacity for the power. The original version was also divided into male and female halves, though I would be in favor of discarding this."