To summarize and expand upon the original suggestion and several others that have come up (note, this contains a lot of my own interpretation):
Focus and Control
Magic is a form of energy that can be accessed by anyone, assuming that person has the right qualities. Two main characteristics are related to this: focus and control. Focus indicates how much magical power a being can actually call upon, and control determines it's ability to shape this raw power into something useful.
Both focus and control have a natural component, but they can be amplified in various ways, depending on the characteristics of the creature. This means that someone who has little natural focus could in theory become very powerful when given the right kind of stimulant. However, someone who's focus has been boosted strongly might not have enough control to actually shape it to their will, possibly resulting in a lot of fun.
The stimulants that can amplify control and focus depend highly on personal and racial characteristics and affinity for stimulants might develop over time. Here's a proposal of how this could be divided, though it's by no means complete:
In general, elves are more susceptible to natural substances, poetry and fine gestures.
Humans use many gestures, combined with words or sentences with mystical meaning. In general they are also more susceptible to gems and precious metal.
Dwarves are most susceptible to runes as well as different metal and stone types.
Goblins draw a lot of power from bones and meat and are also very susceptible to shiny objects.
Which stimulants a person is susceptible to is also very dependent upon their surroundings when they learn magic and what they come into contact with under pressure, though this may also affect it in a bad way.
The actual process of magic
Magic involves calling upon the free magical energy that is available and in general using one's body as a cataclyst. This means that someone with a high focus must also be able to contain and channel the energy and that the use of magic puts a big strain on the body and soul. As said, the use of magic costs as much constitution as actually doing it, though the drain is spread in another way and the mind is more capable of handling the strain.
Calling upon a God is a good way to ensure that you can channel the energy in a safe way. A god can either directly grant the request (which happens rarely) or aid the user by giving them the means to channel and contain magic needed to generate a similar effect. This means that priests relying on their gods must still be skilled in the way of magic to maximize this potential, and they need to have a very strong bond with their god, or else he might not help
Using magic in this way also means that the body itself must be able to contain the magic. Magic users drawing upon the plane of fire to create a gout of fire will generally burn themselves, though the damage can be limited by feeding the magic through the fingertips or using other objects as focal points, even though it's not possible to completely eradicate the problem.
These focal points are usually light objects that can be pointed and held far from the body (for safety measures), meaning most magic users use a staff or wand (usually containing or made of a stimulant), even though a spear would also do. Pretty much any object could be used when it's in a good position or the magic user is skilled enough to channel the energy in the right way. Casters can of course aid each other by focusing their energy into the same focal points to generate effects a single magic user could not create, but this means that each of the casters must be trying to achieve the exact same effect, or else the spells will interfere.
As said, when creating a magical effect in any way, the caster must be able to imagine the process and the effect. Usually this requires a lot of knowledge, though many things can be learned through trail and error, especially when it comes to destructive effects and effects that change the properties of objects.
One last interesting thing about focal points is that it is possible to partially focus an effect into it. The spell has been evoked but not yet completed. This means that anyone who is capable of focusing enough energy into the focal point can unleash the spell. The amount of energy a magic user can focus before a spell actually "goes off" depends largely on their skill level. A champion magic user can imbue items in such a way that even someone who's completely oblivious about the ways of magic can use it.
Potions work in a similar way. They are a combination of stimulants that are known to generate specific effects in most and they are imbued with additional spells. The net effect of this combination is that the consumption of a potion will directly unleash the spells inside, at least in most cases. This also means that many potions are race specific and some are gender specific.