Noumenia
Welcoming the new month, Noumenia is the first day of the new calendar month in the Attic (Athenian) calendar. It is the second day of the three-day festival of Hekate's Deipnon, Noumenia and Agathos Daimon. It's held to honor household Gods, cleanse and clean as well as honor ancestors.
Noumenia is the holiest day of the month. Traditionally, it was held as a day of rest and feasting for ancient Athenians. Men were also said to hold wrestling matches. It is said in Sparta that Kings held out meats and barley for citizens.
Gods worshipped during this day include household gods Hestia, Zeus Ktesios, and Zeus Erkeios. External Gods to aid in calamities were Hermes, Hekate, Apollon Agyieus, Apollon Noumenios and Selene.
Traditionally, a hymn was sung to honor Selene as she began to wax. The hymn can be found here.
Traditional Offerings:
Honey Cakes
New Moon Water
Incense
Flowers / Seasonal Decor
Fresh Meals
Refreshing the Kadiskos and Khernips
Wine
Traditional Acts:
Baking
Cooking a family meal
Wrestling
Cleansing and cleaning
Making Monthly Khernips
Many modern Magissas (Witches) and Hellenic Polytheist revive their homes with a cleansing this day, invoking Hestia and any other Patron Gods/Goddesses.
Links:
Noumenia – Hellenion
Noumenia - Wikipedia
https://www.theoi.com/text/homericahymns3.html#32