This question has been asked quite a few times on AskHistorians, I have also answered a Similar Question a while ago in regards to the pre-Christian Roman method of tracking the years. Much of my answer here can also be found in my other answer.

It is first important to note the current method of tracking years in the west (i.e the Gregorian Calendar) is to use BC (Before Christ) or BCE (Before Common Era) to refer to events which occurred before the birth of Jesus, and AD (Anno Domini "In the Year of Our Lord") or CE (Common Era) to refer to events which occurred after the birth of Jesus. The Gregorian Calendar is not universal. Other cultures use different events to base as "Year 1", (The Hebrew Calendar bases it off the Biblical year of creation, and the Muslim calendar base it off of the migration of Muhammad from the city of Mecca to Medina). The concept of basing year 1 on a single event is not recent, either, as the Romans sometimes tracked years off of the legendary founding of the city of Rome by Romulus. 

Generally speaking, years were kept track by whichever monarch or leader was ruling over the location the chronicler is writing in. In Roman sources for example, the years are either distinguished by which two consuls were in office in the Roman Republic, as consuls were replaced each year; Suetonius commonly chronicles years using the consular method. If a Roman historian were to describe an event from 59 BC, it would be distinguished by a comment such as "This event occurred in the year of Caesar and Bibulus".  Alternatively, during the Roman Empire period for example, the years could also be distinguished by noting whichever Emperor was in charge that year, and how long they had been ruling for, if an event occurred in 22 BC for example, you may see something like "This event occurred in the fifth year of the reign of Augustus". The method of determining years based off of whichever ruler was in charge was common in many cultures. In the Hebrew Bible for instance, when discussing the invasion of Jerusalem by the Babylonians, it is described as occurring "In the ninth year of [Zedekiah's] reign" (2 Kings 25:1).

The BC/AD method of tracking years was first proposed by Dionysius Exiguus in the sixth century AD. The calendar would not become widely used until the eighth century, when the English historian Bede also used the birth of Jesus as a reference in his Latin work Ecclesiastical History of the English People.

I hope my answer helped!

Sources

 “Dionysius Exiguus.” Encyclopedia of World Biography, Encyclopedia.com, 25 Dec. 2019, https://www.encyclopedia.com/people/history/historians-european-biographies/dionysius-exiguus.

Fiorentino, Wesley. “Bede.” Ancient.eu, Google, 10 May 2017, https://www.google.com/amp/s/www.ancient.eu/amp/1-15989/.