D&D's magis system is a set of rules. Rules that govern combat and frequency of use. Rules that govern environmental modifiers and random chance. Just plain rules for almost every concievable situation.
The how is up to the Dungeon Master.
There are no hard and fast constants. It's all environmental and subject to the setting. Some worlds like the
Forgotten Realms have large magical colleges and roaming teachers. Magic is accepted and wizards are scholars. In
Dragonlance magic is a restricted art controled by a single monolithic organization that regulates use and teaches its members spells and the like.
In both cases how the wizards learn magic is vastly different. One might be approached by a mage or offered an apprenticeship while another might find a place in a sanctioned magical school. One might learn spells crafted by ancient wizards or penned by powerful dragons while the others learn the controlled Art as handed down by the gods. In one the mages use the arcane language of dragons to manipulate the Weave with the other has them speaking Magius and controling the power of creation left over from the forging of the world.
In
Ravenloft, the default seems to always be to assume a more Real World approach. Wizards learn their magic from old tomes and scrolls, leftover books from a forgotten time. I've always assumed there are few new spells created and all magical knowledge has to be wrested from time, rediscovered and remembered.
A wizard might stumble down the path of magic after accidently discovering a book of spells in an ancient library. As they progress in their career they understand more of its secrets.
They search for more books of knowledge, adapting what they find and attempting to make it useable.
Does a magic missile always look the same or does a wizards personal style of magic shape it.
Which do you prefer?
There are no rules that control such cosmetic details. If you feel the missile (or any spell) is an extention of personaly of subject to individual modification, then why not? If you think that magic is controled and limited and shaping it would be difficult then say no.
The only guideline I can offer is that any cosmetic change should in no way convey a benefit another cosmetic change would not. A player suggesting that, because his magic missile is shaped like an arrow, he can fire the spell through a small slit is stretching the spell.
It's your world, do what you want with it!