Those who wanted to know their destiny had to ask for the information from the gods. They did this through an Oracle.
What Is An Oracle?
An Oracle could be a person, a thing (such as a shrine) or even just a place. It's connection with the gods was sometimes clear but sometimes obscure. Many Oracles were situated in hard to find places that meant a difficult journey to reach them - the idea of overcoming obstacles to achieve enlightenment can be seen as allegorical rather than literal.
The same could be said of their advice. Oracles rarely answered questions directly, preferring cryptic or downright misleading responses. The answer was always true, but sometimes worse than useless. This tradition of prophecies being misleading is reflected in the famous line from the witches in Shakespeare's Macbeth: "Macbeth shall never vanquished be, until Great Birnam wood to high Dunsinane hill Shall come against him."
One of the most famous historical oracles was the Oracle of Delphi. What was the Delphic Oracle? The term actually refers to the Pythia, the chief priestess at the temple to Apollo in Delphi.
The Pythia was believed to have the ability to tell the future through her connection with the gods. She was often consulted - for a price, of course. However the predictions she gave were often ambiguous and at worst misleading. Some commentators go as far as to say that Pythia simply spouted drug induced nonsense which other priests tried to mould into some sort of sense.
An example of an ambiguous Delphic prophecy is her statement to the Roman Emperor Nero:
The number 73 marks the hour of your downfall!
Nero reasonably interpreted this as meaning that he would die aged 73 - since he was only 30 at the time he assumed he had a long life ahead of him. However the very next year there was a revolt that resulted in Nero taking his own life and being succeeded by Galba - who was 73 years old.
So strong was the reputation of the Oracle at Delphi that the word 'Delphic' has come to mean any statement that is (possibly deliberately) ambiguous or obscure.