The calendar commonly used by the modern Hellenic communities is the Athenian, aka the Attik Calendar, referring to the general region of ancient Greece where Athens resided.
Each month's new moon phase possesses a number of Holy Days, starting on the first day of the new moon, with each one being a specific time of sacrifice to certain Gods or a particular God, Spirit or Hero. They are as follows:
First Day - All Gods.
Second Day - Agathos Daimon.
Third Day- Athena.
Fourth Day- Aphrodite, Eros, Hermes and Herakles.
Sixth Day- Artemis.
Seventh Day - Apollon.
Eighth Day - Poseidon and Theseus.
The Attik Calendar follows a 12 month period, and each month is specifically named for its purpose.
January - Gamelion (Marriage or Wedding)
8th, sacrifices to Apollon Apotropaeus, Nymphegetes, and the Nymphs.
9th, sacrifice to Athena.
12th, Lenea, Festival of Dionysos.
16th, Lenea ends.
27th, Theogamia, Zeus and Hera's marriage celebration, with additional sacrifices to Kourotrophos, Zeus Teleius, and Poseidon.
February - Anthesterion (The Blooming Time)
2nd, sacrifice to Dionysos.
11th - 13th, Anthesteria, Festival of Dionysos.
23rd, Diasia, Festival of Zeus Meilichios.
March - Elaphebolion (Deer Slayer)
6th, Elaphebolia, Festival of Artemis Elaphebolos.
8th, Festival of Asklepios.
10th - 17th, the Great Dionysia.
April - Mounikhion (Great Hill of Munichia)
4th, Feast of Eros.
16th, Mounikhia, Festival of Artemis.
19th, Olympieia, Festival of Zeus.
May - Thargelion (First Loaf or Pot of Grain)
4th, sacrifices to Leto, Pythian Apollon, Zeus, Hermes, and The Dioskouroi.
6th, sacrifice to Demeter.
6th - 7th, Thargelia, Festival of Artemis and Apollon.
16th, sacrifice to Zeus Epacrios.
25th, Plunteria, Festival of Athena.
June - Skirophorion (Final Harvest)
12th, Skiraphoria, Women's Grain Festival of Demeter.
14th, Dipolieia, Festival of Zeus.
July - Hekatombaion (Offering of 100)
4th, Aphrodisia, Festival of Aphrodite and Peitho.
15th, Celebration of the Unification of Attika.
28th, Panathenaia.
August - Metageitnion (Change of Neighborhood)
15th, Games of Eleusis.
16th, sacrifice to Hekate and Artemis.
18th, Games end.
20th, sacrifice to Hera Thelchinia.
25th, sacrifice to Zeus Epoptes.
September - Boedromion (Divine Aid)
5th, Genesia, Festival of the Dead.
6th, Kharisteria, sacrifice to Artemis Agrotera.
7th, Boidromia, Thanksgiving to Apollon.
18th, Epidauria, Festival of Asklepios.
27th, sacrifice to the Nymphs, Achelous, Hermes, Athena, and Gaia.
October - Pyanepsion (Cooking of the Beans)
5th, Proerosia, Festival of Demeter.
7th, Puanepsia, Festival of Apollon.
8th, Theseia, Festival of Theseus.
11th, Thesmophoria, Women's Festival of Demeter and Persephone.
13th, festival ends.
30th, Khalkeia, Festival of Hephaistos and Athena.
November - Maimakterion
21st, Festival of Zeus Meilikhios.
December - Poseideon (Poseidon)
8th, Poseidea, Festival of Poseidon.
16th, sacrifice to Zeus Horios.
19th, Festival of Dionysos.
26th, Haloa, Festival of Dionysos and Demeter.
31st, festival ends.