Throughout the history of the Hellenic empire, various groups of Gods were formed by the people. These groups oversaw a single event, guarded the same thing, or were otherwise linked and worshipped together. It's important to be aware of these ties so when you worship one, you can pay homage to the others as well. The basics of this are taken from

The Theoi Agoraioi
These are the Gods of the agora, the marketplace. Zeus, as the God of kings and princes, presided over the assembly that took place at the agora, alongside Athena, as Goddess of wise counsel, Dike (Justice), Themis (Custom) and Calliope (Eloquence). The Gods of the marketplace, on the other hand, were and are led by Hermes, the God of commerce, along with Hēphaistos and Athena, the patron Gods of artisans: weavers, potters, metalworkers, sculptors, etc. Apollon is another God of the marketplace.

The Theoi Daitioi
These are the Gods of feasts and banquets. Dionysus, the God of wine, and Hestia, Goddess of feasting, preside over these. They are accompanied by festive Gods such as Aphrodite, Goddess of pleasure, and the Kharites, Goddesses of joy, dancing and other amusements. The Theoi Mousikoi, or Gods of music, also accompany the feast.

The Theoi Gamelioi
These are the Gods of marriage. The first of these are Zeus, Hera, and Aphrodite, but others included Hymenaios (Wedding Song), the Erotes (Loves), Peitho (Persuasion), the Kharites (Graces), Eunomia (Good Order), Harmonia (Harmony) and Hebe (Youth).

The Theoi Georgikoi
These are the Gods of agriculture. Demeter is their leader, but for the most part these were non-Olympian Khthonic Gods. These include Gaea, Hades, Hekate, the Horae (Eunomia (Good Order, Good Pasture), Eirene (Peace, Spring), and Dike (Justice)), Persephone, and Ploutos (as God of Wealth).

The Theoi Gymnastikoi
The Gods of the gymnasium, athletics and the Games. They include Hermes, Heracles and the Dioscuri. Nike (Victory) and Agon (Contest) were also counted. Eros, as the God of comradeship, was also frequently worshipped in the gymnasia.

The Theoi Halioi
These are the Gods of the sea led by Poseidon. Several of the other Olympian Gods had minor maritime roles including Apollon, Artemis, Aphrodite and the Dioscuri, who preside over embarkations, harbours, safe voyage, and salvation from storms. Most of this class of God, however, were non-Olympian marine divinities. These include: Amphitrite, Leucothea, Nereus, Palaemon, Phorcys, Pontus, and Tethys.

The Theoi Iatrikoi
The Gods of medicine and healing. These belong to the train of Apollon and included his son the medicine-God Asklēpiós, and His family: Epione (Soothing), Hygeia (Good Health), Panaceia (Curative), Aegle (Radiance), Iaso (Healing), Aceso (Cure) and Telesphorus (Accomplisher).

The Theoi Ktesioi
The Gods of house and home. They are led by Zeus protector of the home (Kthesios) and of the family courtyard (Herkeios) along with Hestia, the Goddess of the hearth. Hekate, Apollon and Hermes were also important household Gods who protected the gates and entranceways.

The Theoi Mantikoi
These are the Gods of oracles, divination and prophecy. These are led by Apollon, the God or oracles and seers, and Zeus, the God of fate. Other oracular Gods included the Titanesses Phoeibe (at Delphi) Themis (at Delphi and Dodona), Dione (at Dodona) and Mnemosyne (at Lebadeia). The God Hermes presides over certain primitive forms of divination including the casting of stones, coin-throwing oracles, and astrology. Lastly Pan and the Nymphs inspire(d) the rustic prophets.

The Theoi Nomioi
The Gods of the countryside and country pursuits, including hunting, fowling, fishing, and the herding of cattle and sheep. They are led by the Olympians Artemis (for hunting), Hermes (for herding) and Dionysus. The rest of the rustic gods are mostly non-Olympian divinities. These include the Ourea (as Gods of the Mountains), the Potam (as Gods of the Rivers), Rhea Cybele (Goddess of the Mountains), and Silenus.

The Theoi Mousikoi
Gods of music, dance and education in the arts. They are led by the Olympian twins Apollon and Artemis, the former presiding over music and poetry, and the latter over the choirs and dances of girls. Other important musical Gods include the nine Muses, the dancing Kharites or Graces, and the musical demi-Gods Hymenaeus and Linos. Dionysus, Hermes and Aphrodite are also Gods of music and the arts.

The Theoi Polemikoi
The Gods of war. These are led by Ares and Athena, and included Gods such as Enyo, Eris (Strife), Nike (Victory), Deimos (Terror) and Phobos (Fear). Zeus, as the God of fate, and Apollon, as God of archery, also had wartime functions.

The Theoi Thesmioi
The Gods of divine law and custom. These are led by Zeus Nomius (of the Laws) and Demeter Thesmophorus (the Law Bringer). Lesser Gods in this sphere included the Horae, specifically Dike (Justice), Eunomia (Good Order), and Irene (Peace), their mother Themis (Custom), and Apollon.