This is a simple little ritual that I try to do each month when the moon is full. I prefer to do this ritual outside if at all possible, even on cloudy nights, or inside at a window from which the moon is visible if outside isn't an option.
I begin the ritual by lighting some incense. I often just use sticks or cones of jasmine, gardenia, or other white flowers. For those who prefer lose incense, the Orphic hymns recommend burning aromatic herbs such as bay, lavender, basil, rosemary, thyme, mint, lemon balm, and chamomile.
I take a few moments to focus myself, and then I recite the Orphic hymn to Selene (hymn number 9):
Hear me, O Divine Queen,
O light-bringing and splendid Selene,
O bull-horned Moon,
crossing the air as you race with night.
Maiden of the beautiful stars,
waxing and waning,
feminine and masculine,
luminous, lover of horses,
mother of time, bearer of fruit,
shining in the night,
all-seeing and vigilant,
surrounded by beautiful stars,
you delight in the quiet
and in the richness of the night,
you grant fulfillment and favor
as, like a jewel, you shine in the night.
Long-cloaked marshal of the stars,
wise maiden whose motion is circular,
come, O blessed and gentle Lady,
lady of the stars,
through your own light
shine and save, O maiden,
(Original line is new initiates. I also sometimes replace initiates with devotee/devotees.)
After reciting the hymn a small libation is poured out for Selene. I often just use cool water. While pouring I say something along the lines of, O Selene, may you be well pleased with this offering.
I follow the libation either with my own personal prayers, or more often, silent meditation. After I thank Selene for her presence, and leave the ritual space.