There are a few festivals in the Hellenic world that are almost universally accepted as sacred. Most of what I do is based loosely on ancient ideas about festivals and celebrations of the divine, but some of the holidays I partake of, like the Anthesteria and this, the Eleusinia (The time of the Eleusinian Mysteries) are among those that I try to take more and than my usual number of cues from the ancients.
The Eleusinian Mysteries pose a great problem for the Hellenistoi because, like most of the mysteries, they were so guarded and sacred that their secrecy was maintained even into the Christian Era, when the Church would have had motivation to spill the beans in order to ridicule or demonize the sacred rituals.
The sacred Mysteries of Demeter, celebrated in the town of Eleusis, were among the most sacred and well known of all the pan-Hellenic celebrations in the Hellenic world. From their inception, Greeks from all over the Hellenic world came to Athens to celebrate the Mysteries and many of the rituals, actually ritual preparations, were common knowledge in the Hellenic and, later, the Roman world.
At first only Hellenes were allowed to participate, but as the Hellenes became more of a cosmopolitan people, and later subject to Roman rule, those rules relaxed and only knowledge of the Greek language was required. (One imagines that understanding the Hierophant was important to such a rite)
In ancient times, those seeking the enlightenment of the Mysteries gathered in Athens, and from Athens they walked the sacred way from Athens to Eleusis (Maybe 12 or so kilometers) and fasted. The trek, not a short one by any means, the exhaustion, the lack of food, and the trials faced along the way, such as mock brigands and such, were meant to remind the people of Athens, and Greece in general, of the trials and tribulations faced by the people as they settled the Greek world, perhaps as they grew out of the dark ages after the fall of Mycenaean civilization.
We are reminded that Demeter gave man the secrets to the cultivation of crops, and in so doing gave them the ability to settle and become a civilized people. We are reminded of the cycles of life and death and of the place of man and the gods in this eternal cycle.
The Eleusinia, as I see it, commemorates the advent of Autumn, the season of reaping what has been sown. The mysteries celebrate the two goddesses, Demeter and Persephone, mother and daughter, and in so doing offer up a link between generations, between life and death, between the present and the future in a chain that is part of who we are as a people.
As a festival commemorating this season, I celebrate it at its beginning with a three day festival. I buy three candles in scents reminiscent of the season, like Pumpkin, and light them one for each day. They stay lit until they expire. I buy and cook foods of the season. I honor Persephone with meditations of sombre character and give thanks to Demeter and Gaia for the bounty of the Earth.