The form of magic used by most human sorcerers is known as the magic of the Old Religion. It is the magic of the earth itself, the essence which binds all things together and maintains the balance of the world.
Rules and Beliefs
The magic used by most human sorcerers and sorceresses comes from the Old Religion. In some way, the essence of magic coincides with the Old Religion itself. The Old Religion is, in fact, not only considered to be a simple belief or worship, but an animated or almost living essence or force of the universe, that holds everything in balance. In the episode Le Morte d'Arthur, Nimueh told Merlin that "the Old Religion does not care about who lives and who dies, only that the balance of the world is restored": this indicates that the High Priestess regarded it as an animated force with a will of its own.
Balance is indeed the key tenet of magic and the Old Religion: in order for something to be taken, something must be given. This is very clear in the rituals related to the power over life and death (Le Morte d'Arthur) or the blood sacrifice (The Darkest Hour), where a life is required.
Even to cast simple spells, there's probably a price to pay: the energy the sorcerer conjures into the world may correspond to a minor quantity of energy drawn from him. Also to negate or destroy magic, magic of an equal power must be used. This was shown, for example, at the end of Merlin and Morgana's magical duel (A Servant of Two Masters): after having summoned a powerful whirlwind that threw the Witch through the air, Emrys collapsed from the effort.
The magic of the Old Religion allows to weave power into the fabric of the world, making solid what it is in the mind, and un-solid what it is already solid. Dragoon the Great, in fact, described magic to Arthur with this words: "Magic is all around you. It's bound to the very fabric of the world" (The Wicked Day).
Practitioners and Followers
The Old Religion is, in fact, the very essence of nature, of the universe and humans who possess the gift of harnessing this energy to their own can shape it at their will. The more they can get in contact with the power of the Old Religion, the more they can achieve and conjure into this world. Therefore creatures of the Old Religion, like Merlin, possess an incredibly strong power, for this very energy lies within them. Merlin, in the episode The Sword in the Stone: Part Two, declared that he was born with magic, possibly indicating that this power is part of him. The High Priestesses or High Priests, because they dedicate their entire existence to serve the Old Religion, have a great access to its power too. In fact, Nimueh, Morgause and Morgana all showed incredibly strong magic.
Unless the sorcerer or sorceress is extremely highly gifted (or his emotions are heightened), like Merlin or Mordred, humans must channel their power with rituals, spells and other instruments of magic. In Series 3, Morgana, having only learnt how to control her magic but not how to use it, had to rely on an object of some sort - such as when she tried to kill Arthur by using a Phoenix Eye and a poppet (The Eye of the Phoenix) - as the central focus for her spells rather than simply conjuring something on her own.
Magic, however, can be performed in other ways, when the conjurer is linked to the power of the Sidhe (Sidhe magic) or trolls (Troll magic). But the Old Religion still remains the source of every power.
A particular form of magic was practiced by the followers of the Old Religion while they were praying the old gods. When Sefa arrived at an ancient building (possibly a place of worship) in the woods outside Camelot to meet her
father Ruadan, she heard him recting a kind of spell ("Crungon walo wide, cwoman woldagas, swylt eall fornom secgrofra wera, wurdon hyra wigsteal westen stapolas, brosnade burgsteall. Betend crungon hergas to hrusan. Forpon pas hofu dreorgiad, ond paes teaforgeapa tigelum sceaded. Crungon walo wide, cwoman woldagas ond paes teaforgeapa tigelum sceaded hrostbeages hrof..."), which was probably the same call for victory over the enemies of the Old Religion that Gaius found written on a piece of parchment, hidden inside an amulet that Ruadan wore around his neck (Arthur's Bane).