Magicians are "wielders" of magic. But in truth, they can only summon spirit slaves and the slaves provide the magic that the magician wields. The spirits come from another realm known as "The Other Place".
Magicians have been described as the ruling class perpetually throughout human history in the dominant nations of the world, and currently rule the British Empire. (Click to see the List of Magicians)
Magicians had no supernatural abilities of their own, they attempt to appear that they do via the use of spirits, which they dubbed demons. By using spirits of different species and hierarchy, the magicians were able to call upon all sorts of powers to their wills.
It has been expressly pointed out that the only true ability of the magician is their knowledge of summoning and binding, which they must do to be able to call up and control their spirits correctly; a single word uttered or wrong move will leave the magician to the hands of the demon, with an almost certain chance of death, and none too pleasantly. In this way, higher magicians likely have photographic memories, discipline, or other such mental capacity, which could be seen as a special ability.
John Mandrake certainly had, or something very close to, a photographic memory, as he showed the ability to memorize several languages, hundreds of summoning arts, a host of binding and disciplinary spells, and could take in multiple clues and details of his environment, all at a very young age.
It should be noted that one did not necessarily have to be chosen as a magician to have the same abilities, enough knowledge is only needed. Kitty Jones learned enough and was able to summon Bartimaeus.
When a child is five years old, the parents could take their child to the government and give them up for a predetermined amount of money. An older, senior magician would then be called upon to take the child as their apprentice. They would have no name for several years because a magician's birth name would give any enemy magicians, or indeed a spirit, great power over the child as they grew up. The child would be trained in several arts, such as geography, history, music, art, mathematics, English, and possibly a few languages until their 12th birthday, at which point they would choose a name from an almanac compiled by the government. Once named, the mentor magician takes a greater role in the younger magician's education, and the child would take several more languages. When the mentor magician believes that they are ready, they take a place in the government, typically at a low level.
Once a magician reaches adulthood, they take their place within the government at a level appropriate to their magical and, usually, work capabilities. For instance, Julius Tallow appeared not to be well adjusted to his detective role in the Ministry of Internal Affairs, though seemed a fairly capable magician, not including the two separate mistakes that turned his skin yellow, and killed him. A magician at this point must be very careful of enemy magicians, as they all vie for power. Magicians usually attain the top job, in the case of the British Government, the role as Prime Minister, by staging a coup d'etat, two of which have known to be performed. A magician must also be careful that they do not point themselves out as a threat too ostentatiously, or voice their opinions too loudly if they differ from that of the upper echelons.
Shamans were a form of magician whom differed from regular magicians in the manner in which they operated. Where as mainstream magicians typically feared and oppressed spirits into service, shamans typically treated spirits with a certain reverence. Bartimaeus once described shamans as so different from regular magicians that they barely deserved to be lumped together in the same category.
Despite generally treating spirits better than mainstream magicians, shamans were not above utilizing them for various purposes.
Shamans to the north of Egypt were known to have a spell that allowed them to leave their bodies and commune with spirits on an equal footing.