There are three ways to see your question. The first, the simplest is to count the years since the foundation (a date that varied of a few years around -750 through time before Varro reconstructed the date of -753. That's the roman era that was still in use in books about roman antiquity until the 19th century. They would probably also make a distinction between the royal period and the republican period.

Another less known division today is an adaptation of the greek system of world hegemonies. We find that system in Herodotus as he makes the Assyrians the first world empire succeded by the Medians and then the Persians. Others continued that ideas with the spartan and the theban hegemony on greece, but those were took out of the list when Alexander conquered the persians. In the second century Polybius wrote his "Histories" to explain how the romans conquered the world in less than 50 years. Later during IInd or in the first century someone named Aemilius Sura (not known otherwise) wrote that Rome is the master of the world since they had subdued Carthage and beated Philip V of Macedonia and the Seleucid Antiochos III (Hannibal had fled to his court after the second punic war), two hellenisitic kings descending from generals of Alexander the Great. Even if the Romans had not conquered all of their territory, the idea that none in the mediterranean were strong enough to try to rivalize with the Romans was enough to proclaim world dominance.

One last idea is the age concept seeing the history of Rome as the life of a man. The royal period is the infancy, the republic is youth and the imperial rule is the old age. But that pessimistic vision criticizing the imperial rule was adapted at the beginning of the second century into a new youth, a clever way to please the emperor Trajan.

Are you asking did the romans set up eras like we tend to do like the 'Dark Ages' etc?

Just because when reading the question i would answer it differently depending on either reading the title or the description.