This is a fun one. Taking AD 20 as our example:

Dating conventions varied widely in the first-century Near East. The Romans famously dated the years by the (ordinary) consuls. So if you happened to be roaming the colonnaded streets of Caesarea Maritima (capital of the Roman province of Judea) and asked some toga-clad passerby the year, he would say - doubtless with a supercilious gaze and dismissive tone - that it was the year of (Marcus Valerius Messala) Barbatus and (Marcus Aurelius Cotta Maximus) Messalinus. Only an historian would know or care to tell you that it was 773 Ab urbe condita (years since the foundation of Rome, by the scholar Varro's reckoning).

If instead you asked inhabitants of the Greek cities seeded through Palestine by the Hellenistic kings, you would receive very different answers. Many of these cities still used the Seleucid Era, which counted (more or less) from the date Seleucus I seized Babylon and embarked on his imperial career. On the terms of this era - used in some places until the eighth century - AD 20 would be the year 332. Many individual cities had their own eras, which commemorated events ranging from their conquest by Pompey to the creation of the province of Judea. For cities that counted from Pompey's conquest, AD 20 would be the year 83.

Although Jewish practice seems to have varied from community to community, the most common convention (despite widespread distaste for the memory of the Seleucids themselves) was the Seleucid Era. The years of local rulers' reigns were another point of reference. Jews living in Galilee, for example, might refer to AD 20 as the 24th year of (the tetrarch) Herod (Antipas).

So if you built a time machine, went back to AD 20, found Jesus, and asked in your best Aramaic what the year was, he - as a Galilean Jew - would probably have told you the year of Herod's reign, or perhaps the Seleucid era.