The Greek oracle was consulted by individuals and by states on questions of war, colonisation and cult, and what made it function politically was the very ambiguity for which it is now mocked.
The Pythia
At Delphi the office was held by the Pythia, a woman of Delphi who responded to enquiries on fixed days in the temple of Apollo. She was not understood to be interpreting; the tradition held that Apollo spoke through her. Priests were present, and the relationship between what she said and what the enquirer received in writing has been argued over since antiquity, the ancient sources themselves disagreeing about how much shaping went on. She served for life once appointed and was required to remain celibate during her tenure.
Ambiguity as a feature
The answers determined colonisation, war and cult foundation across the Greek world, and the classic case is the reply to Croesus, that if he crossed the Halys he would destroy a great empire, which was true whichever empire fell. The ambiguity was not a defect but the mechanism: an oracle that committed to a plain prediction could be shown wrong, while one that spoke in riddles retained authority whatever happened. Geological work since the late 1990s identified faults beneath the temple emitting hydrocarbons, offering a possible mechanism for the ancient reports of vapours, though the finding is contested and does not settle what the participants understood themselves to be doing.