Vance actually explains his magic system in the foreword to Rhialto the Marvellous. A spell, in Vancian magic, is a series of words, thoughts, and actions that attract a response from a supernatural entity that can sense them. These entities aren't necessarily intelligent, or even sentient. They range in power from minor madlings, through the quarrelsome sandestins, to the lesser daihaks. Temuchin classified the daihaks as a category including both 'demons' and 'gods.' When the magician constrains a spell in memory, the words in the brain throb with energy; this is the entity noticing that the first part of the operation has been completed. When the caster releases the spell, the entity performs whatever action the spell was related to, perhaps infusing an area with fire or a deluge of acid, or perhaps it merely removes carbon dioxide from the caster's lungs and replaces it with oxygen.
Each spell is different and precise. You can no more "modify" Rhialto's Green Turmoil to produce fire, than I can suddenly turn my sweat into drops of gold. Experimentation is fraught with dangers; while many of the more popular spells call on entities with the mental power of plankton, more potent entities can provide more potent effects, and are generally more mischievous and unreliable.
As a result, the most powerful magicians reduce their reliance on spells in favor of direct control of the supernatural entities in question. Different methods are required for each entity, and many remain unknown; Temuchin's disappearance (and the sudden reappearance of different body parts identified as coming from his still-living body, that have appeared in myriad places in the thousands of years since then) is believed to have been caused by his experiments regarding control of the daihaks. Most sorcerers prefer to use sandestins, who can be controlled by the use of chugs*, although not often with perfect success.
* chug: a semi-intelligent type of sandestin, which by a system too intricate to be presently detailed, works to control the sandestins. Even use of the word 'chug' is repellant to the sandestins.