Homer begins his Iliad as Hesiod begins his poems, by invoking a goddess, probably a Muse (although Homer, unlike Hesiod, does not specify).
A similar kind of divine revelation is embodied in the character Calchas, a prophet...
"who had knowledge of all things that were, and that were to be, and that had been before, and who had guided the ships of the Achaeans to Ilios by the gift of prophecy that Phoebus Apollo had granted him."
Again we have divine knowledge granted by a god, and this knowledge encompasses the past, present, and future. And like Hesiod, Calchas magically knows about seafaring, although it is not his trade.
In the story of Troy, Apollo also grants Cassandra the gift of prophecy, along with the curse that nobody will ever believe her.
Sometimes ancient Greek prophets would spontaneously realize their prophecies. Most, however, would interpret their prophecies from various omens: dreams, the arrangement of entrails, and animal behavior.
Aside from any claim of divine authority, such divination can be thought of as a form of praxeology. It implies that events in the universe can interpreted as willful actions of divine agents.
The diviner saw patterns that other people could not understand. The layman had to trust the expertise of the seer. King Agamemnon went so far as to sacrifice his own daughter on the authority of Calchas.
Our most pernicious modern-day diviners are climate scientists. They too look oh-so-carefully at the patterns in nature that the layperson cannot understand (climate statistics in their case), and pretend to be able to infer from them judgments of great consequence.
Next in this series: Thales and Deductive Geometry.