Thought I'd chime in.
There's magic in my conworld. In early years, it occurred as random events due to it not being fully understood. Many specialists (shamans, medecine men, etc.) emerged and made use of their knowledge to find applications to magic. Then, a few people actually spent their life studying the properties of magic and at least one of them wrote a book (called the Codex or Gwaurne Qaadesh, the "book of knowledge") in which precise details about the practice of magic are found. She wrote it after having teached this practice to many students for a few years, so it was usable material for those left behind. She divided it into four areas:
- telekinetics, the ability to move matter without seemingly applying force on it
- atomics, the ability to manipulate atoms, molecules, etc.
- pyshics, the ability to manipulate minds
- dimensionics, the ability to manipulate space
Magic comes from an ever-present matter, kind of like the aether, called the samri. In order to use magic, it is necessary to absorb samri in one's body to stimulate the brain and then cast the spell. The issue is that one's body isn't made to survive a lot of samri absorptions, notably because it tends to fuse within arteries and veins, eventually blocking bloodway. Some species are more apt to samri absorptions because they evolved in samri-high environment and they thus make the perfect candidate for wizards.
(Local samri depletion isn't a problem while not dealing with batshit crazy wizards willing to absorb huge amounts of samri to cast one spell and die; in any case, life in the perimeter would die because of samri loss)
Absorbing samri requires channels made of certain materials, like samrigit (a stone with a high samri concentration) or other minerals, plants or even living tissue with high samri levels. These are embedded in the skin, virtually anywhere works. The absorption is a voluntary act -- the channel doesn't drain samri inside one's body passively. So, to make the channel work, some magic knowledge is required. Before they were invented, wizards ingested samri food, which took a while to stimulate the brain.
The actual process of spellcasting is complex as it obeys to rules one must learn or create. While there are a limited range of effects to produce through magic, the processing to get the effect must be imprinted in the brain through a lot of practice. It requires a lot of control, concentration and anticipation. The use of symbols, movements and other tools ease the control and concentration requirements and it may be widely different from one "school" to another. Some wizards may use incantations to streamline their thoughts and produce the desired effect, while some other would use movements, either fingers, hands, arms or all of them at the same time; even dancing. The actual practice produces an association between what one does and what happens. This is why wizards always repeat the same thing to produce the same effect. There is no discrete component in an incantation that hints to the effect being a fireball.
A great deal of studies of magic is to study other schools in order to predict spells one could face in their life. This usually involves a lot of espionage from school to school. Also note that "school" is the word I use but it doesn't necessarily imply Harry Potter-like settings. In some culture, for example those in which wizardry is taught only to one's children, the school would be the "family teachings". But yes, there are Harry Potter-like settings, big schools with many students learning magic and usually two or more "schools".
The domain of dimensionics is special because it requires one to predict what will happen to one's body. When, say, trying to open a hole to access an object behind a wall, you can't just open it, put your hand in and feel the area to try and locate the object. Doing so would without doubt give you nausea, headache and probably nosebleed; worse case, seizure or brain hemorrhage. There exists a martial art based on dimensionics. In its region, it is regarded as one of the most beautiful and the hardest feat. It requires a lot of anticipation, both of where your punch or foot will end up related to your opponent but also to where you need to block (or to divert through another dimension-hole) your opponent's next move.
There also exists a few means to increase the amount of samri locally in order to gather more to stimulate the brain longer. Freeing gaseous samri or cutting open people are common practice.
Some things aren't possible to do: raising the dead, calling upon spirits, ... Off of the top of my mind.
I don't think I forgot anything. Feel free to ask questions