The Athenian calendar is the best known and most intensively studied, and I shall therefore use it as a model. The Athenian months were named Hekatombion, Metageitnion, Boedromion, Pyanepsion, Maimakterion, Poseidon, Gamelion, Anthesterion, Elaphebolion, Munychion, Thargelion, and Skirophorion. (For a list of the known month names in other Greek areas, see Ginzel, vol. 2, pp. 335-6). The intercalary month usually came after Poseidon, and was called second Poseidon. Hekatombion, and hence the beginning of the year, fell in the summer. Other Greek regions started their year at different times (e.g., Sparta, Macedonia in fall, Delos in winter).
For the historian inclined towards tidy orderliness, the regrettable fact is that the Athenians were simply unwilling to stick to a completely regular calendar, which makes reconstruction difficult. Their irregularity was not from lack of astronomical knowledge. In 432 BCE, the Athenian astronomer Meton instituted his 19-year cycle, fixing regular intercalations (whether Meton got this cycle from Babylonia or discovered it himself is not known). From that point, a small group of Greek astronomers used the Metonic cycle in their calculations, but this should be regarded as an astronomer's ideal calendar. Abundant epigraphical evidence demonstrates that in the civil calendar, while the archons inserted approximately the correct number of intercalary months over the long term, the specific corrections were somewhat arbitrary, as the archons saw fit. This irregularity doesn't really affect the long-term workings of the calendar, but it does make things very confusing when trying to establish a precise date for an event.
The Athenians seem to have taken a rather casual attitude towards their calendar. It appears they used neither a regular formula nor continuous direct observation to determine the length of the months. Most likely, they followed a general rule of alternating months (29 and 30 days long), subject to periodic correction by observation.
In addition to this calendar, which has been called the festival calendar, Athenians maintained a second calendar for the political year. This "conciliar" year divided the year into "prytanies," one for each of the "phylai," the subdivisions of Athenian citizens. The number of phylai, and hence the number of prytanies, varies over time. Until 307 BCE, there were 10 phylai.
After that the number varies between 11 and 13 (usually 12). Even more confusing, while the conciliar and festival years were basically the same length in the 4th century BCE, such was not regularly the case earlier or later. Thus documents dated by prytany are frequently very difficult to assign to a particular equivalent in the Julian calendar, although we are usually secure in assigning an approximate date. Since the prytany will play no role in my argument for establishing a basic chronology, I will not go into the intricacies here. The references cited below, however, go into the problem in mind-numbing detail.
Ordinary records of Greek city-states were dated according to the eponymous year of the person in power, be that the archon, king, priest of Hera, etc. For Athens, our list of archons from the 4th c. BCE to the later 1st c. CE is complete for all but a few years, which is a great help in verifying our chronology. Regional eponymous years, however, are awkward for historians trying to correlate the various areas, a problem no less evident to the ancient Greek historians than it is to us. The solution that seemed obvious to them was to reckon time by the intervals between Olympiads, in addition to giving eponymous years.
That the Olympics were held every four years is well known, but some evidence for that assertion is not out of place. Ancient writers all refer to the Olympics as a 5-year period (in Greek, pentaeterikoi, Latin quinquennales). This might seem strange, but Greeks and Romans most commonly counted inclusively; that is to say:
1 2 3 4 5 Olympiad . . . Olympiad
which we would call a four-year interval. NB: our way of counting implies a zero start, a concept both Greeks and Romans lacked. Since the Greek calendars all differed slightly, you might wonder how everyone managed to get to the games on time. The Pindar scholiast claims that for the early Olympiads, the festival was held alternately after 49 or 50 months, which is essentially equivalent to four years in a lunisolar calendar. This scheme makes perfect sense, because no matter what specific intercalary months the various cities did or did not decide to include, they could all simply count forward to 49 or 50. It also implies, by the way, that a rule of 8 years = 99 months was being used to determine this interval (although not that every Greek city used this formula for their own intercalations).
Since the Olympiad was a summer festival, it was eventually correlated to the Attic (Athenian) calendar, so as to begin on Hekatombion 1, which might imply a certain agreement about when intercalations should be added, or simply indicate Athenian cultural dominance.
Ancient historians date by Olympiad by giving both the number of the Olympiad and the year within the cycle, 1-4 (the Olympiad itself was held on year 1). Additionally, lists of Olympic winners were maintained, and the 3rd c. BCE writer Timaios compiled a synchronic list comparing Olympic winners, Athenian archons, Spartan kings, and the priests of Hera from Argos.
Olympiad 1,1 correlates to 776 BCE. We do not actually need to believe an actual festival was held on this date, but when Greek historians are writing in later times, they date their own events using this as the epoch. We can establish a precise correlation to the common era from a variety of different sources, but the most definitive comes from a passage in Diodorus, where he dates the year of a total solar eclipse to the reign of the Athenian archon Hieromnemon, which he also gives as Ol. 117,3. The only astronomically possible date for this event is August 15, 310 BCE, which fixes our epoch.
One thing to be wary of with reckoning by Olympiad is that writers calculated the start of the year by their local convention (spring, summer, winter, or fall). For example Ol. 1,1 correspond to Fall, 777 - Fall 776 BCE by Macedonian reckoning. Byzantine writers who use Olympiads take the year to begin on September 1.
Most of the other eras used by Greek writers are of little importance. One worth mentioning, however, is the Trojan Era (from the destruction of Troy), which is found in a number of historians' works. This date, of course, is purely conventional, and can be seen as analogous to the various world eras (e.g., Hillel's above). A wide variety of starting points are found, but the one with the widest currency, developed by Eratosthenes, set it 407 years before the first Olympiad (1183 BCE).