Following the birth of Apollon during the Delphic Polythousia (or the Theban Prostateria) that occurs on the 7th day of the Delphic month Bysios (derived from Pythios) or the Theban month Prostaterios (Anthesteria to people who are only familiar with the Attic calendar lol) in the this month following (reminding you all that I am a month ahead of most people by my calendar since I celebrated Poseidon II last year) this month (Attic Elaphebolia) honors the slaying of the dragoness Python and the narration of the myth of the return of Apollon next month.
For those who are not familiar with the myth, Apollon following his birth, arrived at Delphi. There are two variations of this myth. One in which he has come as a grown man, and another in which he and Artemis are carried to Delphi by their mother. There he encounters to the guardian of the stream Castilla. In the Homeric hymn to Pythian Apollon we find a description of Delphyne as a great bane of a creature who is a plague bringer and devourer of flocks. Apollon slays her either with his golden sword or with his bow, either alone or with the aid of his sister (as all of these versions exist). He (or they in the case of Artemis as well) departs Delphi in sorrow, weeping in his exile. Myth has it that as he leaves for Hyperborea that his tears fall as amber on the earth.
However in the Stepteria we have the program of the slaying of Delphyne acted out in which the youth, standing in for Apollon, slays the dragon. It has been suggested by scholars that this may have either been by throwing a live serpent or effigy of a snake into a structure to burn to death as Delphyne was consumed. So doing, he would flee immediately, taking no part of food or comfort. There he would be at the mercy of strangers as he traveled from town to town with his attendants, acting the role of an outcast in exile before finally arriving at the Tempe Valley. There he would be purified by entering the laurel grove and would cut branches from the sacred laurel at the side of the river Peneios to return with them to temple around the time of the spring equinox to the temple with great celebration.
For this ritual, unless you have a sacred river and laurel trees to act out the exile on a small scale (or the means for roughly a month of camping) the best way I have found to celebrate this ritual is to praise Apollon, the slayer of the serpent, to invite him of the golden sword to liberate and free, to destroy the miasma that infects our homes and cities and regions. Invite the shooter from afar to pour out his arrows as he begins the season of his return. From paper make a small serpent (or out of any other flammable substance) and set this in a fire safe bowl upon your altar, as you do so lighting it on fire as you praise Apollon as purifier and averter of evil, praising him for being Pythios, who causes things to rot and pass away to release all things for new rebirth. You are welcoming here too the dawn of spring as you destroy the fortifying wintry dragon. I then follow this with grieving for the exiled lord Apollon, and grieving for the death of the dragoness as was carried out in Delphi. I pour offerings upon the earth for her even as Apollon does to appease her spirit as he flees.
The ritual should be finished with a simple meal, the fair of exiles without friend or shelter, relying on what little they could manage. A humble meal should follow. Tonight we are having some chicken and roasted potatoes. Simple fare without extras or indulgences. For seven days then I pray to Apollon for his return. On the 21st day of the month that is sacred to him I enact my own ritual that I call the Daphneaia which is about his entrance into the holy grove and his purification by the river Peneios and Daphne. Until then it is a time of reflection, awaiting purifications of the Daphneaia.
Post Ritual Update:
This year I did something a bit different. I had burned the paper serpent in a brass incense burner bowl and watched her dissolve into dust from the flames even as I prayed to Apollon. I had forgotten to mention above that it is appropriate to read from the Homeric Hymn to Pythios, which I did reading the segment of her destruction. Following her destruction I pray to Apollon that that which is miasmatic, that which breeds evil is not in and of itself evil in all entirety and that he cleanses and purifies all things to release us from the bonds. I lamented for Delphyne and lauded her place that she gained as guardian spirit of Delphi as upon her bones the precinct rested. I poured the libation, not directly on the earth this time, but upon her ashes (which will be disposed of upon the earth at some point this evening), lamenting her death as I did so. I then followed as my usual lamentation for his exile that he shall not be among friends, that he departed for the far lands and left all bereft of his presence as he attends to his blessed cleansing.
I then played my wooden flute for Delphyne. In Delphi the youth representing Apollon would as Apollon play the flute for Delphyne as Apollon was said to have done. Its long mournful tones singing to her passing and mourning too his banishment from the company of men.
In the end there are many ways you may come up with to celebrate this festival that will all be spiritually fulfilling and meaningful.