Dream magic
The primary form of magic in the cosmos of Rachoy, dream magic gets its name from the fact that the magical potential used to cast it is gathered through dreams. (That being said, in everyday life "dream magic" is rarely referred to as such—since it's the only type of magic most inhabitants of Rachoy are familiar with, they just call it "magic".) As far as most scholars can tell, during their dreams people—or some aspects of them—travel to some other realm or cosmos, which some refer to as "Magogenia". There they accumulate dream energy they can use to wreak magic when they wake (or, in the case of sleepcasters, unconsciously while they're still sleeping). This theory does leave a few details not fully explained—such as the existence of the ambient magic that seems to exist independent of dreaming—but it fits the facts well enough to have won wide acceptance.
Origins
Rachoy didn't always have magic; dream magic was apparently brought to the cosmos long ago—exactly how long ago isn't clear, but hundreds of thousands of years ago at least—by the being now known as Gomar the Ancient, god of magic. Before Gomar, according to some accounts, there was only one plane in Rachoy, the plane of Charés, and the people there lived and worked without magic to aid them. But then Gomar created Magogenia, and people began to dream, and magic was born.
The accuracy of this tale is disputed—the more so since it exists in a number of different versions that contradict each other in the details—but there is plenty of evidence that there was, indeed, a time when dream magic didn't exist, or at least wasn't known. Be that as it may, nowadays dream magic has become such an important and accepted part of life that it gives rise to the name to the entire cosmos—the "Burdipén Rachoy" means, in a certain language, "World of Dreams".
Associations
The main way that dream magic works is through arcane cause-effect links technically called daracos, but more colloquially, and more frequently, "associations". Associations are essentially the fundamental principle of dream magic. Every way that dream magic is used is ultimately simply a type of daraco—at least, according to many scholars.
Basically, through a daraco, a specific action or process becomes associated with a specific magical result. Thereafter, any time that exact process is undertaken, that result occurs. This simple formula can apply to a variety of different combinations, and the ultimate possibilities for the uses of associations are nearly unlimited.
Spells
One of the most obvious uses of dream magic is in spellcasting. There are many different forms of spellcasting in Rachoy, stemming from different ways that people have found to channel dream energy into their desired effects, but they all come down to the same basic idea: the caster goes through the mental processes required for the spell, and something happens.
Because of the way that spells have developed from each other and evolved over the years, the known spells of dream magic have been classified in a system of carminical taxonomy. Many casters specialize in knowing spells from particular taxonomic groupings; it's certainly easier to learn a group of closely related spells than it is a collection of spells more distantly connected.