Magic is a very real force in the world of Merlin and not something easily defined, magic is power and this power can be used for good or evil. Merlin has for example killed with magic and also healed with magic. Just as Nimueh has plagued the kingdom with her magic it is indicated that in the past she has used her magic positively when she and Uther were friends.
Merlin's eyes glow when he uses Magic
Magic is generally achieved by incantations spoken in old English and written in Runes. However some magicians such as Merlin and Edwin have been seen to use magic without incantations but with simple will power and hand gestures.
Magic is treated as academia to some extent it requires study and mastery, however Merlin's ability to summon magic is instinctual, he simply has to learn his craft already being able to summon magical power. Other gifts exist too, such as Morgana's ability as a seer, her dreams often reveal certain future events. It seems that many people are linked to magic innately and have to learn to harness their power. Though there are people like Gaius who have no magical gift as such but can access their magic through study and hard work. Since magic is a force or energy that can touch or affect the world, but cannot be touch by anything from our world magic is said that only magical energy can destroy or negate magical energy.
Magic is a potent force able to conjure various enchantments and effects such as shape-shifting, telekinesis, slowing down the rate of time, summon fire, summon wind and achieve all manner of results.
There are certain tools of power such as the mage stone wielded by Tauren which has the power of transmutation or the Sidh staff Merlin took from Sophia which can be wielded as a powerful magical weapon.
The spells themselves are varied, Mary Collins used a Poppet to kill Lady Helen which was known European magic falsely imposed on voodoo. Further more Mary Collins used singing to work some of her magic. She sung an enchantment of sleep in her attempt to kill Arthur. it is clear that magic being a broad practice that it cannot be easily put into a single framework and why would you want to after all? Sometimes potions are needed, sometimes magical creatures or objects are sought for and at other times the it just takes the sorcerer alone. A sorcerer will also develop their wisdom and magic, able to achieve things when in their magical infancy.
Another important element of magic is that some of it is ancient and is linked to the old religion. Here magic does not just get used by the witch or warlock but the magic also uses them. That is, there is a cost or demand: when Merlin asks the Dragon to enchant a sword with its fire it has demands that must be met as dragon fire and dragon magic is part of the ancient magic. A better example is that of creating life, where the magic demands a life to be sacrificed for the life to be given.
Magic is potentially dangerous but also beautiful and potentially useful, Uther banning it has created many enemies and Arthur has been raised not to trust magic and sorcerers. However it has been indicated that magic is a part of Camelot, intrinsic to the kingdom so there's a lot we have to learn of magic - it seems that one is always still just becoming a magician.