There seems to be more detail on how the Romans did their paganism as compared to Germans and Celts.
Roman gods and goddesses seemed like Tulpas or imaginary friends. The fact something is imaginary doesn't mean it is not real. The gods and goddesses live in our imaginations and that makes them as real as anything.
Some key concepts in Roman religion.
CULTUS DEORUM. The name of the Roman religion is cultus deorum, this means "care of the gods" or "cultivation of the gods". They would have an idol and make offerings to the idol and keep the idol and a household shrine.
CAPITE VELATO "with head covered" was the manner in which Romans prayed and made offerings to their idols and their gods. This resembled the jewish prayer shawl.
DONATIO: the concept that in order to recieve one must give, it was expected to give offerings to the gods. Sometimes in the form of coins sometimes in the form of libations and candles. THE NUMA TRADITION was a philosophy in Roman religion that was against animal sacrifice. If someone had nothing to offer the gods simple time and attention given to the gods is enough(where attention goes energy flows, attention is a offering)
VOTUM is a promise made to a god. Sort of like "if you do this for me I will build a shrine in your honor" or "I will say hundred prayers in praise of you" or something like that. Relationships with the gods were seen as a sort of contracted where the people kept the gods alive through remembering them and attending to their shrines and in return it was expected the gods were to watch over them in certain ways.
PRECATIO is the Roman term for prayer. Prayers were considered effective even without offerings.
EVOCATIO is the military practice of depriving an enemy of their patron god or goddess. This could be done by telling the deity how corrupt or sinful the enemy is or it could be done by promising(votum) to build the deity an even better shrine, this promise would be done in the hopes of convincing the deity to be on the side of your army.
INVOCATIO is calling upon a deity. often times done along with LIBATIONS.
LIBATIONS are pouring drinks out for deities. People in theghetto often pour out alcohol for their dead homies. The Romans poured out drinks onto the ground for their dead ancestors as well. The Romans kept a shrine in their house for their ancestors and it was considered that ancestors would be starving in the afterworld if no one remembered them(where attention goes energy flows).
PIETAS: The romans felt their good fortune was based on devotion to their gods and that if they deviated from it they could fall into ruin which was called IRA DEORUM(anger of the gods), being on good terms with the gods was PAX DEORUM.
OBSERVATIO was the interpretations of signs and omens. A way of averting a bad omen by explaining it away and invalidating it was called ABOMINARI.
NEFAS was the Roman term for haram. To do something nefas could bring about the wrath of the gods.
An altar is basically a place where the gods are fed, a table for feeding the gods with our attention(where attention goes energy flows).
The Roman author Ovid wrote the story of the gods which you can listen to for free here
https://librivox.org/metamorphoses-by-publius-ovidius-naso-ovid/