State religion was very much centred around activities designed to protect or promote the state, such as in times of war or famine. It was collective worship and ritual designed to invoke the continued protection of the gods for Rome.
Priests ensured that protocols for ritual were followed exactly to ensure that they worked correctly. Priests were also politicians and generals, and priesthoods could be temporary or permanent positions.
You should look for features such as the altar (for sacrifice), a sanctuary area (for purification) and architectural features such as the podium, a cella, a colonnade.
Augurs and haruspices were soothsayers who used different methods to foretell the future. Augurs tried to interpret natural signs such as the movements of birds, whilst the haruspex would read the entrails of animals.
They were the only female priesthood in Rome and attended the goddess Vesta. They looked after the sacred flame, which represented the safety of the state. The temple of Vesta also held important state documents and the wills of important Romans.
The site of Pompeii is very well preserved but may not be typical of a Roman town. It is also frozen at the point of the eruption of Vesuvius, so cannot tell us anything beyond this point in time.