This is from my old blog, The Geekie Hellenist.
This is my Libation to Artemis ritual. Note: All my Libation rituals are the same, the names of the gods have been changed. Enjoy and I hope that this helps.
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 Artemis know that your here. Say, “Artemis, hear me, ‘ then lists her titles (of the wilderness, glorious, she who leads). Of course you can use any of her titles that I have listed in the ‘Titles for Artemis’ section. State why your here, which is to give her her monthly libation that’s due to her, and if she’s done anything in the past. Include any offerings that you have given to her or any deeds that you have done in her name.
5) Do the Invocation to Artemis.
I call to Artemis, fleet-footed bow-woman, roamer in the woodland, wild-willed mistress of beasts, fierce-hearted protector of young girls. Artemis, daughter of thundering Zeus and blessed Leto, sister of bright Phoebus, the lovely nymphs attend you. On Delos and in Ephesos your name was spoken with reverence and devotion; in all the lands your temples stood, ever fragrant with sweet incense. The creatures of the wood gather around you; the graceful dear, the bear and the boar, all are yours. Artemis, friend of the hunter and the fisher, friend of mothers and midwives and all small nurslings, friend of maidens, unfettered and free of spirit, far-shooting goddess, goddess of the strong voice whose words of the heart are heard, I call to you.
6) Do hymns to Artemis
Sing O muse of Artemis, sister and nurse-mate of Apollo the far Darter, Virgin Goddess, who having watered her teamsters at rush grown Meles, swiftly drives her golden car through Smyrna to vine-clad Claros, where Apollo of the Silver Bow sitith waiting for the far-shooting Huntress.
Hail to thee, and to all the goddess with thee, in this my song! I have shall first begin my hymning with thee, and beginning with thee shall pass another day.
7) Do a prayer to Artemis
Fleet-footed Artemis, keen-eyed daughter of Zeus and gentle Leto, sister of bright Apollo, we see your shadow in the woods, the curve of your bow, the flex of your arm, we hear the wind whisper as your arrows seek their mark–deadly your art, flawless your aim.
Huntress you are, O Artemis, slayer of the stag and the boar, slayer of men and of women, death by your hand is death unforeseen.
Maiden are you, goddess, and friend of maidens; ever-youthful one, your favor falls on the young, watching over young girls as they brave the world’s wonders, comforting the mother in the throes of her labor, keeping in your care the newborn babe.
Artemis, shining maid of the wilderness, who takes pleasure in games, in contest and in merriment, who leads the nymphs in their carefree dance, whose clear voice we hear in the songs of young women and the hunter’s cry.
Artemis, strong and tall, I praise and honor you.
8) Offer Incense to Artemis, saying, “With this incense, I honor you. Oh goddess of the Hunt and childbirth. You who helped to birth Apollo.”
9) Pour Libations to Artemis, saying, “With this libation, I honor you. Oh goddess of the Hunt and childbirth. You who helped to birth Apollo.”
10) If you want to, pray to Artemis.
11) End the ritual with a prayer to Hestia.
“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.