Modern Hellenic practice is often described from its festivals, which are public, organised and photographed. The domestic side is where most practitioners actually spend most of their religious time, and it is centred on a household altar and on Hestia.
The pattern reported by practitioners and by researchers who have worked with them is a small shrine at which libations of wine, water or oil are poured, incense is burned, and hymns are spoken or sung, drawn from the Homeric and Orphic collections or composed in their manner. Hestia receives the first address, as she did in ancient practice, before the wider pantheon. Frequency and formality vary a great deal between households, and there is no single liturgy that all practitioners follow.
The organising commitment is reconstructionist. Forms are drawn as closely as the evidence allows from ancient domestic cult rather than composed freely, and where evidence is thin practitioners are generally explicit that they are inferring. Barbara Jane Davy's survey of contemporary paganism and Michael Strmiska's comparative collection on modern paganism in world cultures both describe this method and the debates within the movement about how far inference may go.