I invite you to take a look at the answers to similar questions in the past in the FAQ. Basically, in that period every culture had its own way of designating years.

Nearly all of them were based on regnal years -- the number of years the ruler at the time had been in power -- or eponymous years, designating years by the person who held some magistracy or similar post that changed on an annual basis. In practice both of these boil down to eponymous systems, since regnal years are named for someone who holds an office for more than one year.

Regnal year systems include, for example, ancient China, the Ptolemaic dynasty, and the Roman empire in the time of the principate; eponymous year systems include ancient Athens and republican Rome (and the principate too, until 537 CE when Justinian switched the eastern empire to a solely regnal-year-based system).

The main exception in the western world, where years were counted from a specific event, is the Seleucid year, which counted from the beginning of the reign of Seleucus I in 311 BCE, and which persisted in some areas until the late Mediaeval period. From the 3rd century CE onwards the Hebrew anno mundi system came into being, along with some similar Christian systems; the modern Hebrew anno mundi system dates to Maimonides in the 1100s CE. And from the 4th century BCE to late antiquity, some chronographers used the system of counting by Greek Olympiads of four years each. And some Roman historians in late antiquity counted years from the legendary date of Rome's founding as calculated by Varro.

In the specific case of Cleopatra VII, I don't know that we have any documents from Cleopatra's reign that explicitly cite a calendar era system. The normal Ptolemaic practice was a regnal year system, so the year 45 BCE, for example, would have been designated Cleopatra 6 -- on the propaganda-based claim that her tenure as ruler of Egypt began in 51 BCE. (In reality Ptolemy XIII held a large amount of power until his death in 47 BCE.)