Descriptions of typical Hellenic rituals of sacrifice can be found in the secondary literature  as well as primary texts such as the Iliad.  As modern Hellenes usually do not sacrifice animals, some of the ritual actions particular to blood sacrifice may be modified or passed over.
The key elements of a bloodless offering are as follows:
The participants move from a central gathering place into the sanctuary and up to the altar.
Marking the Space
The offerings and sacrificial implements are carried around the altar. There is a good deal of controversy about whether this should happen in a sunwise direction or not; as there is no consensus within the community on this issue and no incontrovertable historical evidence one way or the other, this detail can be left to the discretion of the ritual leader or group, or omitted altogether.
Preparations for the Sacrifice Proper
In Greek, this phase of the ritual is referred to as arkhestai, meaning "to begin." The hands of the participants are washed with lustral water (khernips). The water may be purified by plunging a piece of smoldering wood from the fire into it  or salt water may be used.  The water is also sprinkled over the sacrifices and altar.
Preliminary Offering of Barley and Prayer of Invocation (katarkhesthai)
Participants take handfuls of barely groats (oulai, oulokhutai). The sacrificer, with uplifted arms, speaks a prayer or other call to the gods. The barley is then thrown onto the altar.
Final Preliminary Offering (aparkhesthai)
Using the sacrificial knife, the sacrificer cuts off a small portion of the offering and casts it into the fire. With animals, a bit of the hair from the animal's forehead was used; a small piece of bloodless food offerings can be cut or broken off.
The Sacrificial Moment and Ululation (he thusia kai ololuge)
The offering is cut, broken, or spilled out on the altar. At the same time, the women give a shrill trilling cry.
Distribution of the Sacrifice
A small (often inedible) portion of the offering is set aside solely for the gods; this is usually burned (for the Olympians) or placed in a pit in the earth (for the Khthonioi). Some sources indicate that the first portion of the sacrifice was offered to Hestia,  and this may be incorporated into the order of the ritual. Small offerings may then be made to each deity associated with the festival. The rest is cooked (if necessary) and distributed among the people. Today this last act may take place at the concluding feast rather than at this moment.
Offerings of wine, milk, oil, or other liquids are poured out onto the fire. In modern usage, potable offerings may be poured into a bowl from which the participant then sips. The remaining contents of the bowl are then poured out onto the fire or the ground.
Conclusion and Call to the Feast
The offerings (and other food) are now shared by the participants. Traditionally all the food was consumed at the ritual site. Modern usage allows for excess food to be taken away or donated to a food bank or other charitable cause.
For an example of a full offertory rite, click here.
 Burkert, Greek Religion, pp. 56-57, upon which my own discussion is primarily based, For details on vocabulary, implements, and techniques of animal sacrifice, see the summary in Bruit/Schmitt, Religion in the Ancient Greek City, pp. 32-34.
copyright 2000 by Andrew Campbell
This article originally appeared on Andrew Campbell's Nomos Arkhaios site which is currently on hiatus.
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