People in ancient Greece believed in gods which acted and thought like humans. This is commonly referred to as anthropomorphism. Unlike Christianity, where God is seen as perfect, all-forgiving, and all-knowing, the gods in ancient Greece were just as fallible as humans themselves. For example, it was not unheard of for gods to fall in and out of love with each other, arguing with each other and behaving in an irrational and jealous manner. The best example for this is the behavior of Zeus, the head of the ancient Greek gods and goddesses. Zeus was married to Hera, but was known to engage in affairs with mortal women. Hera responded to this behavior with great jealousy, which we can see in her horrible treatment of Heracles, for example, who was born following Zeus's affair with Alkmene.
In terms of religious activities in ancient Greece, you might want to mention the fact that it was not uncommon for all the different gods and goddesses to have their own temple or altar. As it was feared that a god might respond with anger towards humans if they were not worshipped as much as other gods, it was very important in ancient Greece to ensure that no god or goddess would ever feel neglected. This led to the erection of temples and altars for various gods and goddesses all over the country. Sometimes, people in ancient Greece would perform sacrifices of animals to please the gods, and priests and priestesses would perform prayers and other rituals in at attempt to communicate with their gods.