Personal worship in the ancient world

This pair of terracotta altars depicts the death of Adonis, a god of vegetation, and the rituals that were celebrated in his honor. On the altar on the right, Adonis, looking weak, sits supported in the arms of his lover Aphrodite, the goddess of love. Adonis was born of an incestuous love between the Assyrian king Theias and his daughter Myrrha; Aphrodite was smitten by the infant Adonis's great beauty and hid him in a box (cista), which she entrusted to Persephone. When Persephone opened the box, she too fell in love with the beautiful infant and decided not to give him back to Aphrodite. Zeus interceded in the quarrel between the two goddesses and ordered that Adonis should spend a third of the year with Aphrodite, a third with Persephone, and the last third wherever he liked— Adonis chose to devote that time to Aphrodite as well. The woman at bottom right, sitting on the box, is likely to be Persephone. On the left altar, three women rush to the scene, carrying musical instruments: a tympanum, or drum, and a xylophone.

Small terracotta altars such as these would have been used for private worship, perhaps to burn incense. This pair still bears traces of burning on its upper surfaces, as well as pigment used for decorating the relief figures. Stylistic features of the figures and their drapery, as well as the type of clay that was used, suggest that the altars were made in Medma, in Southern Italy. - J. Paul Getty Museum

Household shrines and a personal relationship with the gods were also important to the Romans as well.  

"The quality in which the Roman commonwealth is most distinctly superior is in my opinion the nature of their religious convictions… These matters are clothed in such pomp and introduced to such an extent into their public and private life that nothing could exceed it, a fact which will surprise many… It is a course which perhaps would not have been necessary had it been possible to form a state composed of wise men, but as every multitude is fickle, full of lawless desires, unreasoned passion, and violent anger, the multitude must be held in by invisible terrors and suchlike pageantry." - Polybius

Classicist Ben Potter, in his article "Rituals, Temples and Worship in the Ancient World" observes, "Here, the historian seems to confirm that the vast majority of common/uneducated Romans engaged in ritual practice with a high level of credulity and were not merely going through the motions when it came to showing devotion to the gods on days of ritual worship."

Read more about it: https://classicalwisdom.com/culture/traditions/rituals-temples-and-worship-in-the-ancient-world/

Small personal altars depicting the myth of Adonis produced in Calabria, southern Italy, terracotta, fourth quarter of the 4th century BCE on view at the Getty Villa, Gallery 109