The Greeks were worshipers of Nature, and their gods simply represented different aspects of nature and abstract concepts. It was as natural to them as worshiping God is to us.
At their temples.
Gods
Greeks would pick a god that was a patron of their trade or hobbies. A farmer would pay homage to Demeter, a hunter would pray to Artemis, a blacksmith to Hephaestus, a warrior to Ares, a scholar to Athena, a mother to Hera, or a wine maker would worship Dionysus. Also certain times of the year would demand a sacrifice to certain gods.
At temples or by prayer.
Yes,some do!
Most did, yes.
To worship their various gods.
It is in their tradition and it is something they strongly believe in.
burnt offerings and temples of worship
They worshiped a whole pantheon of Gods.
They worship the gods by holding ceremonies to certain gods, and make sacrifices in their honor.
Temples dedicated to specific gods or goddesses.