Hestia is invoked at the beginning and end of all solemn public oaths and sacrifices. At the Prytaneion, townhall, her sacred fire was kept burning as the center of city life. There officials sacrificed to her as in a private home, the father or mother would worship her. Those seeking the state's protection would go to the Prytaneion's sacred fire. Her sacred fire, at the Delphic Temple, was the center of Greek religious life.
The attributes of Hestia include a serious, but gentle expression seen on statues, and a sceptre.
Sources:
Greek Religion, by Walter Burkert
Handbook to Life in Ancient Greece, by Leslie and Roy Adkins
Dictionary of Roman Religion, by Leslie and Roy Adkins

