Magic in the DHS Continuum can be used to do many tasks, from setting things on fire to storing objects in a pocket dimension for later use to healing and even illusions.
There are two ways in which magic is acquired - one is either born with the ability to cast magic in them, or one asks the gods to lend them their power. People generally have to ask the gods for magic, while monsters generally have their own. Animals usually have no magic ability whatsoever. There are of course exceptions, such as the Fey, who are people that create their own magic, and the Griff, who are people who cannot use magic at all.
People often learn magic by attending a shrine school at the temple of the god whose power they wish to use. They can also learn by attending hero schools, and very rarely people are contacted directly by various lower gods and offered magic. People usually have an affinity for one or two gods' magic, but with study they can learn more.
The most popular magic is of course that of the nine magic gods (Jake nonwithstanding), though many of the lower gods have some magic too, and the triad of creation goddesses have the most powerful magic. However, in order to use the creation goddess' magic, one has to utterly devote one's life to them. These people become Light or Dark Powers to gain Sola or Luna's magic, and spend all their time trying to spread the influence of their chosen goddess by fighting the opposing powers. There are also Chaos and Nature Powers for Gaea, but they are chosen by existing Chaos and Nature Powers, and are huge dorks anyway. GaRaLa has no Chaos or Nature Powers.