Someone who is new to the Hellenic religion (whether it be Paganism combined with Hellenistic attributes, or polytheism alone) needs to understand the deities themselves. Here will be the basic understanding and not so in-depth understanding of the Greek deities for those interested in starting out in the Hellenismos. There are hundreds of Greek God and Goddesses, but I'll start from the simplest, the Olympians.
Zeus - God of the Sky, storms, justice, law, order, and fate. Married to His sister, Hera, and son of Cronos and Rhea, the Titan and Titaness.
Hera - Goddess of marriage and women. Married to her brother, Zeus. She was also a goddess of the sky and starry heavens.
Athena - Goddess of wise counsel, war (and battle strategy), the defense of towns, heroic endeavour, weaving, pottery and other crafts. Virgin Goddess, born from the head of Zeus fully armored and ready for battle.
Aphrodite - Goddess of beauty, love, pleasure and procreation. married to hephaestus, and born from the castration of Ouranos, floating over sea foam. Different tales say different things about Her birth, depicting being created from the sea or from Ouranos.
Apollon - God of prophecy and oracles, healing, plague and disease, music, song and poetry, archery, and the protection of the young males. Son of Zeus and Leto, and born on the little island of Delos, along with His twin sister, Artemis.
Artemis - Goddess of hunting, wilderness and wild animals. She was also a Goddess of Childbirth, and the protectress of the girl child up to the age of marriage. daughter of Zeus and Leto, also born on the island of Delos.
Poseidon - God of the sea, rivers, flood and drought, earthquakes, and horses. Also known as the Earthshaker, Poseidon was born of Cronos and Rhea, married to the Sea-Goddess Amphitrite.
Hermes - God of Animal husbandry, roads, travel, hospitality, heralds, diplomacy, trade, thievery, language, writing, persuasion, cunning wiles, astronomy, and astrology. He was also the personal agent and herald of Zeus.
Hephaestus - God of fire, metalworking, stonemasonry and the art of sculpture. Married to the Goddess Aphrodite. Son of Hera and Zeus, casted out when He was a baby because of his deformity.
Ares - God of War, battle, lust, civil oder and manly courage. Son of Zeus and Hera. Although Ares did not have much of a wife, He did have infamous relations with Aphrodite.
Dionysus - God of wine, vegetation, pleasure and festivity. Son of Thebian princess Semele and Zeus. Married to Ariadne (mortal).
Demeter - Goddess of agriculture, grain, and bread, the prime sustenance of Mankind. She never married, but She had one daughter with Zeus, Persephone.
There are other Gods and Goddesses that are recognized as Olympians (such as Hades, Hebe, Hestia, ect.) but never spent Their time on Mount Olympus. There are others who do spend their time on Olympus, such as husbands, wives, cupbearers, and so forth.