They made offerings at the altars of temples and made animal sacrifices, usually the thigh.If they had a certain problem or wish, they would go to a certain God's or Goddess' temple. For instance, if...
because the Greeks could not think of anything scientific. they then thought that all things that happened must of been something that had great powers, immortals they called them.
People worship gods for many reasons, perhaps originally because this gave them some control over their lives. They could call on their gods to ensure a good crop, a victory in war, help in a crisis...
They would worship their gods. They would sacrafice animals and place them on the altar at the temple. The temple for some gods had a statue of them in it. All the gods apparently "controlled nature".