Our modern calendar is BC and AD - say I lived in the year 100 AD. What year would I say I live in? What point in history or event was I counting up from?
Different people did it in different ways. I'm most familiar with Rome. In common use years were designated by the names of the consuls - so "in the year of the consulship of Caesar and Bibulus" for instance. Some Greek cities did something similar. Athens for a while used eponymous archons. This sort of dating logic also pops up in the gospel of Luke when the birth of Christ is dated to the rule of Quirinius in Syria.
A similar method (still used in some Japanese documents I've had to deal with randomly in a non-academic context) is regnal year: In the 4th year of the reign of Emperor So-and-so. Obviously keeping all the magistrates in the correct order can be tricky, and at Rome Augustus dealt with this difficulty by inscribing the "official" order of consuls in fasti, lists of the official order of consuls. You can still see them in the Capitoline Museum if you like.
Obviously this kind of dating is awkward, and by Augustus' time historians like Livy had started writing histories that referenced the founding of the city as the starting point for the timeline, abbreviated in Latin as AUC (ab urbe condita - from the founding of the city). The traditional date for that is 753 BCE - Varro's date - but other historians had other dates so you can still get your years crossed up depending on which historian you read.
Another common system in the Greek world was to keep track of time by Olympiads. Olympic games were held every four years, traditionally beginning in 776 BCE, and people could refer to and event that happened in, say, the 2nd year of the 57th Olympiad.
hi! you'll find some examples in the FAQ