Greek religion is unusually well documented and unusually easy to misread, because almost none of the documents were produced in order to explain it.
Poetry and drama supply most of the myth. Homer and Hesiod were old and authoritative but not canonical, and later poets and tragedians reworked their material freely. There is no single correct version of a Greek myth, and the same story was told differently in different cities, often to suit local claims. Reading these texts as though they were doctrine produces a tidy pantheon that no Greek would have recognised.
Inscriptions are much closer to practice. Sacred laws set out who may enter a sanctuary, what may be sacrificed, which portions the priest receives, and what a worshipper must do beforehand. Accounts record temple property; dedications name the giver and the occasion. This material is dry and intensely local, and it is the best evidence there is for what people actually did.
Archaeology supplies sanctuaries, altars, votive deposits and animal bone, which sometimes confirm the texts and sometimes contradict them. Philosophers are evidence for educated criticism, not for common belief. Later writers such as Pausanias, travelling in the second century CE, described sanctuaries and their stories at a point when much of what he saw was already antique.
Two consequences follow. Athens is heavily over-represented, because Athenian texts survive in quantity, so the standard picture is skewed toward a single city with an unusual literary output. And the interior of the practice, what a farmer took to be happening as he poured a libation, is essentially unrecoverable. Statements about what the Greeks believed are, with few exceptions, statements about what the Greeks did.