Tolkienian Magic
Magic in the Legendarium is a complicated matter. Notwithstanding that, like in all things, Tolkien oft changed his mind on what magic was able of and more importantly for our discussion on who is able to wield magic, the Legendarium is meant to have been written by Hobbits who are prone to label everything they don't understand "magic". Galadriel herself is not sure why the same word is employed for the arts of the elves and the deceits of the enemy. Yet magic certainly exists in Arda, even in the form we know of. The elves of Nargothrond and the Green Elves are said to have defended their hidden fortresses by spell and poisoned darts and Gandalf once knew all spells of closing and opening in the tongues of Elf, Man and Orc.
So what is magic. Well we are going to make a distinction between Magic and Sorcery there. The latter being used only to express what Morgoth and Sauron and the rest of the Umaïar do and teach.
The first form of magic is simply some innate ability of the wielder. The elvish féa, their soul, is able to exert itself at some distance, acting in the Unseen world. Thus, they are able of little miracles according to human standards like seeing in the minds of others and spying the pattern of their thoughts. In the lords and ladies of the Calaquendi who saw the light that was before the sun and moon, this power can take impressive proportions indeed. While Galadriel's control over Lorien is enhanced by her mastery over Nenya, she would be able to forbid the borders of her domain even without the Ring of Water as she is simply sending her féa outwards, making it an obstacle for any who would penetrate it. The Valar and Maïar beings built entirely of spiritual matters are able to exert their might beyond the boundaries of distance and Morgoth claimed that even the shadow of his thoughts could have tangible effects for the people he hated.
Now that form of magic is exclusively the province of an immortal, or someone whose féa has been unnaturally tied to their hroa or body. For mortals are born to leave the world and are not bound to it like the Powers and the Firstborn (That doesn't mean you can't make predictions about Men but they are always able to act against them). I count the Dwarves among the Immortals because even if they die of old age their féa seems to abide in the world, as they think they are meant to dwell in separate halls in Mandos. Still the main use of their féa seems to be infusion into items.
Men, like any other living creatures can use spells. Spells are reflections of the Great Music who came before the world. They are harmonics who can change the world for after all on some level Arda is music. When Tom Bombadil declares "His songs are stronger songs" he is boasting of his superiority in magic. Such spells can be learned even by a mortal but it requires a life to be able to manage more than small effects and even then such magic tends to enhances things rather than create them. A blessing pronounced upon a batch of athelas would increase its curative proprieties while a group of adepts could chant to banish a wight. The lesser the adept, the stricter the rhythm of their spells should be. (I'm not going to do that but imagine all spells by normal humans must be in iambic pentameter or some other closed verse)
There I would make Dwarves a mid-point between Men and Elves, while they learn spells quicker than Men and have more people able to do "magic", their spells are only reflecting the Music of their creator Aulë and the themes and objects found therein. There again, craft would be the most common use for these spells. Something like chants to be sung over the forge to bless the item you are making or the like.
The third and last wholesome form of magic is Craft. All thinking beings were given the Sacred Fire by Eru. The Dwarves were adopted by the creator and whatever Morgoth did to create the Orcs he couldn't touch the divine flame within them just like he couldn't give it to anything he created rather than twisted into being. This flame means every living creature have the power to sub-created and there comes the magic of craft. A part of the essence of the crafter can pass through them to the item they forge. This is not like the One Ring but rather like the lifeforce of Miriel passed to her son Féanor. Even Men can create such masterworks but only once in their lives and after they can't make them no more. Most renowned weapons are the products of this and of spells.
And then there is Guldur or Morgul, that none of the Free People will aknowledge or practice. Guldur is composed of spells who reflect and influence the essence of Morgoth present in Arda either through the original Marring or through the dispersion of his essence through the First Age until the earth herself became his Ring. Unlike wholesome magic Guldur is rather easy to learn. The catch is that, for a mortal practitioner it requires blood and pain, preferably taken from unwilling sources. Pain, anguish but also foolish pride and black despair are echoes of the Discord, false notes and silence in the melody of creation. The Nazgul are of course the greatest masters of these black arts but they have a tendency to spread anywhere and anytime people are dissatisfied with the slow progress of normal magic.
Canonical examples of Morgul are the spells wrought unto Ghrond, the ram who broke the gates of Minas Tirith and the incantations that book-Witch-King howl before each strike. The creation of Barrow-Wights is also an effect of Guldur as this sorcery allows the adept to confers with both Unhoused and Umaïar. The timely storm who sunk the ship of the last king of Arthedain and the Great Plague of the Third Age (as well as others, Morgoth and Sauron love sending plagues on their greatest foes of the moment)
