Today, we'll talk about some Greek and Roman methods of fortune-telling, interpreting omens, and divination.
One method of divination was to pay a fee at the temple of Hermes, then whisper a question into the statue's ear. The person would then plug his ears with his fingers until leaving the temple. When he was outside the temple, he would unplug his ears and take the first remark he overheard as an answer from the god.
Astrology was, naturally, a very common practice. This seems to have originated in Babylonia, when the activities of heavenly bodies were recorded and compared against events happening on earth in order to ascertain what might happen in the future. The Mesopotamians associated each planet with a god. The Greeks substituted these with their own gods. The stars were assigned to constellations which told stories of heroes and monsters.
Natal astrology, the idea that the time and place you were born could affect your life on a personal level, was encountered by Herodotus in Egypt during the fifth century BCE.
It's a short one this week, but I'm sure that gives you plenty to research.