Most oracles are unique. They can look like anything from a ragged old woman to a beautiful person surrounded by all the fine things money can buy. (Most oracles re female)
The Sybaline oracles of Rome wrote it down on scrolls. The Delphi oracle spoke. Some went into trance and raved, others spoke very clearly, but were not believed. (Most oracles spoke, but often someone was right there to write it for them)
Either in a remote, secluded place, or in a temple where many people came. Or they might be out in the general population, just being normal until the prophecies came.
Anyone can see/hear an oracle. Some of them were hard to reach (living out in the wilds) and others were expensive (in their own temple, with entry fees)
Some just start raving. Others have a set ritual. Some take some sort of drug. Many only give prophecies when the prophecies come. (My favorite for this is Sybill Trelawney from Harry Potter. She is very much a classic oracle)
Some oracles go around begging someone to believe them, others charge a lot for their services. It all depends.
Since this is your story, pick what seems interesting to you. Or make something up. As a writer, you have the power to do this.