We currently count years with Jesus' birth as the reference point, year 0. But for people living before him, or right after his birth, what was their point of reference.
For example, in what year would Plato say he was born?
I can't comment on greek systems of year naming, but in ancient mesopotamia, the year would be names based on the king ruling, and named after something notable the king did that year.
See here: http://cdli.ucla.edu/tools/yearnames/yn_index.html
This question actually comes up a lot. Timekeeping varies by culture, of course. Check out these threads. I can also speak to the Roman system, but others have done it better: in brief, the Romans in the Republic would reckon from the mythical founding of the city (ab urbe condita), and add the names of the city's magistrates for the year.
So: Julius Caesar was born (most scholars agree) in 100 B.C.E., or, the 654th year ab urbe condita, in the consulship of Marius and Flaccus.
The dating system gives rise to some good old-fashioned Roman jokes: in 59 B.C.E., Caesar is said to have so overshadowed his co-consul Bibulus that people would refer to the year as "in the consulship of Julius and Caesar" rather than "of Caesar and Bibulus" (source: Suetonius, Life of Caesar 20).