This is a great question. The Romans had many religious practices and they even boasted that they were one of the most religious people on earth. For this reason, they believed that the gods were favorable towards them. Let me list a few of the most common religious practices of the Romans.
First, the Romans had many ritualistic practices to ensure the favor of the gods. They sacrificed to the gods, held games and festivals to the gods, and prayed the gods. The important point to keep in mind is that the Roman were meticulous in their practices.
Second, before any important action, such as a battle or some other campaign, they would see if the gods were favorable. In essence, they were looking for a green light. To do this, they took auspices. This basically meant that they would look at bird patterns to see if the gods were favorable. They also sometimes looked at the entrails of animals to determine the favor of the gods.
Third, the Romans also looked at prodigies or omens as a sign that the gods were not pleased. They expiated these odd or out of the ordinary events (like a flood or heavy rainfall) to restore the pax deorum, which is called the peace of the gods.