This is from my old blog, the Geekie Hellenist.
This is the ritual for Apaturia. Well the way that I celebrate it. You can change things to suit you but this is for Zeus and Athena. Hope that you enjoy this ritual and have a great night.
1) Purify the Altar area.
2) Take the barley and say, “As it was done in ancient times. I purify and cleanse this altar with this barley. With this barley I purify this altar and space so that I may give offerings, libations, and speak with glory and respect the gods of Mt. Olympus.”
3) Light a candle and say a hymn to Hestia.
Hestia, you who guard the sacred shrine of the Lord Apollon. The far-darter at goodly Pathos. With soft oil dripping ever from your locks. Come now to this house, come having one mind with Zeus the all wise-draw near, and with all bestow favor upon my song.”
Prayer to Hestia
Hestia, gracious goddess who sits at the heart of each home, who lives in the heart of each one who reveres you, each one who holds you dear, each one who turns to you for strength and harmony.
Hestia, goddess most needful, goddess most serene, goddess most esteemed, the heart of the city is yours as well, great goddess; within your realm are those who serve the state, who work for all the good of all–your blessings fall on the honest, goddess, your wrath on the corrupt, on those who betray their trust for gain. Defender of the householder, guardian of the hearthfire, Hestia, I praise and honor you.
4) Let Zeus know that your here. Since this is to honor Zeus Phratrius then direct your greetings to him in this form. (Note: I’ve been trying to figure out what Phratrius means but I haven’t been able to find out).
5) Do a Invocation to Zeus
I call to great Zeus, father of the deathless gods, ruler of bright Olympos, master of storms, child of mighty Kronos and deep-hearted Rhea, consort of blessed Hera of the splendid eyes. Ancient Zeus, honored in Crete so long ago and well known in high-reaching Arcadia, all-knowing Zeus of Dodona and Didyma whose wisdom was granted to seekers of old, Zeus of the broad sky, Zeus of the marketplace, Zeus of the householder, Zeus of the city. Protector of the just, avenger of the wronged, friend of the stranger and of the traveler, friend of the guest and the generous host. Zeus whose eye is ever on the world, whose hand is ever in our lives, great Zeus, I call to you.
6) Do a Prayer to Zeus
Father Zeus, defender of cities, defender of homes, defender of the traveler, of those far from home, of those who rely on the refuge of civilization; kindly Zeus who watches the world, friend of the fates, giver of good fortune, by your good will are our larders full, our children strong, our minds and bodies sound and vital; Zeus, from whom all good derives, whose gifts are sought by all, who knows our troubles and our joys, who hears our calls, who answers them with wisdom and with care; oh Zeus, whose wrath falls on the wrong-doer, whose blessings come to those who are fair-minded and good of heart, who stands behind the guest and the stranger, I praise you!
7) Do a hymn to Zeus
I will sing of Zeus, chiefest among the gods and greatest, all-seeing, the lord of all, the fulfiller who whispers words of wisdom to Themis as she sits leaning towards him.
Be gracious, all-seeing Son of Cronos, most excellent and great!
8) Let Athena know that your here.
9) Say an Invocation to Athena.
I call to Athena, clear-eyed daughter of Zeus; from his head you burst forth, all in brilliant armor, a warrior from your first breath, born with all the skill, all the insight, all the guile of an old warlord.
In ancient times were you well honored, goddess; in every town your name was spoken with love and reverence; above all in Athens, the finest of cities, did you receive the greatest devotion.
Bolt Athena whose favor falls on the brave and on the clever, who hones the wit of the scholar and quickens the nimble fingers of the artisan, who offers counsel reasoned and reflective, farsighted builder of cities who leads humanity towards concord and community, granter of the gift of civilization, I call to you.
10) Say a prayer to Athena.
Glorious Athena, whose spirit stands so tall and strong in shining cities, whose comfort is sought by great heroes and by those who aspire to greatness, whose courage and cleverness are without equal, gracious Athena, I honor and revere you.
Athena, advisor of kings and queens, granter of wisdom to those with wit to seek it, goddess whose eye is ever fixed on the horizon, goddess who is open to all possibilities, goddess who is aware of all options, goddess who in every game thinks ahead to its every ending.
Athena, mistress of the long view, I call to you to show me what will be, I call to you to guide me through the world’s intricacies.
Athena, steel-eyed goddess, I sing of your might, I praise your name, I thank you for your many gifts.
11) Sing a hymn to Athena.
Of Pallas Athena, guardian of the city, I begin to sing. Dread is she, and with Ares she loves deeds of war, the sack of cities and the shouting and the battle. It is she who saves the people as they go out to war and come back.
 Hail, goddess, and give us good fortune with happiness!
12) If you want to add anything to this ritual, something that goes along with what Apaturia is about, then you can do it at this time. You might want to introduce your baby to the gods or a child who wishes to follow the gods.
13) Give Food Offering, saying, “I offer this food as a sacrifice, to you Zeus and Athena.” Note: If your child is taking part in this then she or he can give an offering of food as well.
14) Pour libations to Zeus and Athena. Remember: Hestia gets first and last libations. Note: If your child is taking part in this then she can pour libations to Zeus and Athena as well.
15) Pray to them. Either as an individual or a group.
16) End the ritual by saying, “Hestia, goddess of home and hearth, to you I offer last of all as a pious mortal should. Tend to those whom I love and guard the houses of the pious. As the gods will it, so it shall be.”
It is so!
Dump the entire container that you’ve poured your wine or grape juice into outside and then that ends it.