In addition to large-scale civic sacrifices, replete with ceremony, historians tell us of a wide range of other devotional activities in pre-Christian Hellas. No one type of offering was mandatory for all situations, although prayer, whether including hymns and liturgical elements or spontaneous and heart-felt, was inseparable from offering.
Private home life, for instance, typically involved bloodless daily sacrifices of edibles, such as bread (with various ingredients and shapes, fruit, cakes, vegetables, and things cooked for normal consumption, as well as spices. Through flame, the gods received the scent of the offerings.
Additionally, tables consecrated for the purpose and placed next to altars served as offering tables.
Libations, about which much is written elsewhere, had common implements and simple procedures. In a common form of libation, one would pour from a jug of consumable liquid, such as wine or milk (most commonly wine of the consistency usually consumed by people of the day, but could even be a mixture of wine with honey), into a shallow bowl of a type from which one could drink. An offering of the liquid would then be poured from the shallow bowl onto the altar or the ground. The rest would then be consumed.
These same basic forms of Hellenic devotion are practiced today. In practice, they are most likely impacted by the passage of time, space, and culture, but one may, with a little care, proceed with confidence that one is in keeping with the most critical elements of tradition.
For more information on the subject matter of this post, see Religion in the Ancient Greek City by Zaidman and Pantel.