It's a thing that comes up a lot in literature, but I never found an explanation of how that process worked. As far as I know, the priests involved had 'real world knowledge' such as of places suited for settlement, therefore they didn't just derive their answers from religious rituals.
Every oracle was different in its source, from the laurel-chewing Delphic priestess to the rustling oaks of Dodona, or the dreams sent by Ascelapius.
But in common, questioners made donations and priests interpreted the results to them. Let's concentrate on the Delphic oracle as one of the best-described.
Most questions had simple answers. When Xenophon left Athens to lead mercenaries for the rebel Persian prince, he asked to which gods he should sacrifice to ensure his success. His friend told him later that what he should have asked was if this were a good thing to do in the first place. So most questions had yes/no or otherwise simple answers.
Tricky poems were for matters of state.
And, yes, the interpreters at various times tried to control politics. Herodotus remarks that the Oracle was Medizing, favoring the Medes, in the Persian Wwars, and giving messages urging the defiant Hellenes to give up.