Although there were some atheists among the ancient Greeks, Greek religion pervaded community life. It wasn't a separate sphere. People didn't take breaks each day or once a week to pray to the gods. There was no synagogue/church/mosque of Greece. Personal, privately-held belief wasn't important; public, ritual performance was. While some practitioners of specific mystery cults may have looked to their religion as a way to attain the Afterlife, entrance to Paradise or Hell did not depend on one's religiosity. Religion dominated most events the ancient Greeks participated in. In Athens, more than half the days of the year were (religious) festivals. Seemingly (to us) secular events, like athletic festivals (e.g., the Olympics), and theatrical performances were held to honor specific gods.
The Greeks were polytheists. There were many gods, although each city had its own particular protector. Athens was named for its main goddess, Athena Polias ("Athena of the city"). Athena's temple on the acropolis was called the Parthenon, which means "maiden", because the temple was the place to honor the virgin goddess aspect Athena. The Olympics (named in honor of the home of the gods) featured a temple to Zeus and annual dramatic festivals were held to honor the god of wine, Dionysus.
Greek religion focused on sacrifice and ritual. Priests cut open animals, removed their entrails, burned the appropriate sections for the gods and served the remaining meat to the people.
When making prayers, priestesses poured libations of water, milk, oil, or honey onto a flaming altar. Prayers would be offered for favors or help. The help might be to overcome the wrath of a god angry at an individual or community. Some stories tell of gods offended because they were omitted from a list of gods honored with sacrifice or prayer; other stories tell of gods offended by humans boasting they were as good as the gods. Such wrath might be demonstrated by the sending of a plague.
Stories told about the gods and goddesses, the mythology, changed over time. Early on, Homer and Hesiod wrote accounts of the gods, as later did playwrights and poets. Different cities had their own stories. Unreconciled contradictions didn't discredit the gods.
Not only did each city have its protector deity, but its ancestral hero(es). These heroes were the half-mortal offspring of one of the gods, usually Zeus. Many of the Greeks' anthropomorphic gods lived active lives, primarily different from mortal lives in that the gods were deathless. Such stories about the gods and heroes formed part of the history of a community.
"Homer and Hesiod have ascribed to the gods all things that are a shame and a disgrace among mortals, stealing and adulteries and deceiving on one another."
~Xenophanes
