The worship of Hestia was less flashy than that of the other major gods. She had few temples dedicated specifically to her. Pausanias tells us of two: one at Hermione and a sanctuary dedicated to her at Sparta. She seems to have had no major festival*** and was more often depicted as a flame or a hearth fire than in human form.
[Detail of Hestia & Demeter on a kylix vase, 5th century BCE, Antikenmuseum, Berlin]
Little is known about Hestia’s priesthood. The only major example we have is an inscription in praise of the goddess by a priestess of Hera who spent some time as chief priestess of Hestia at Ephesus. She praises Hestia as the preserver of fire without whom the gods neither eat nor drink. There is some reference to the “Hestia of the City” of Sparta, whether that was a ceremonial position or an actual priesthood remains in doubt. In Roman times she may have been a member of the city assembly.
Hestia may have been one of the quieter goddesses in myth, but she was also the most widely worshiped, for none could do without her.
*The other two, Artemis and Athena, probably did and in their early incarnations were likely interpreted as virgins not because they never took lovers, but because they never submitted to monogamous marriage. This, however, was soon erased and they were worshiped as virgin goddesses in the current sense of the word.
**Unlike her Roman counterpart Vesta.
***The Acropolis at Athens, for example was dedicated to Zeus as chief of the gods, Athena as protector of the city, and Hestia.
Homeric Hymn 5 to Aphrodite - Perseus
Homeric Hymn 24 to Hestia - Perseus
Homeric Hymn 29 to Hestia and Hermes - Perseus
Inscr. Ephesus 1062 G, found in Lefkowitz & Fant no. 24 (Inscription by priestess of Hestia, not available online)
Pomeroy, Sarah B. Goddesses, Whores, Wives, and Slaves. New York: Schocken, 1995.
Hestia - Theoi.com
Hestia - Wikipedia