It really depended on where you lived but commonly it was based on the ruler or important figure through synchronic dating. For example Thucydides wrote in book 2 about the start of the Archidamian war,

“The thirty years' truce which was entered into after the conquest of Euboea lasted fourteen years. In the fifteenth, in the forty-eighth year of the priestess-ship of Chrysis at Argos, in the ephorate of Aenesias at Sparta, in the last month but two of the archonship of Pythodorus at Athens, and six months after the battle of Potidaea, just at the beginning of spring, a Theban force a little over three hundred strong, under the command of their Boeotarchs, Pythangelus, son of Phyleides, and Diemporus, son of Onetorides, about the first watch of the night, made an armed entry into Plataea, a town of Boeotia in alliance with Athens.”

So you see here he is reckoning time based on the time of a priestess, an ephor, an archon and an important event and it was up to the reader to triangulate when this event took place. The closest you get to something like a year count may be the Roman “ad urbe condita” which reckoned the date from the founding of Rome, however there it was more common to reckon the date from who was consul that year.