The Romans did not count days in the month as a simple number, as we do, but backwards from one of three fixed points in the month: the Kalends, the Nones, and the Ides. The Kalends are always the first of the month. The Nones fell on the 7th day of the long months (March, May, Quinctilis, October), and the 5th of the others. (Note that this long-short distinction refers to their length in the republican calendar, not the later version.) Likewise, the Ides fell on the 15th if the month was long, and the 13th if the month was short.
The very earliest calendar used by the Romans is obscure. By later Republican times, however, it is, if not regular, at least well documented. From the time we have direct evidence of it, the pre-Julian calendar was roughly lunisolar. Certain Roman religious customs, as well as the monthly subdivisions of Kalends, Nones, and Ides, indicate that the calendar was originally lunar, and that months began upon direct observation by a priest of the new moon.
Of all ancient calendrical systems, the Greek is the most confusing. The Greek Calendar is much like ancient Greece itself. It shared a certain basic similarity from region to region, but each city-state kept its own version. All the Greek calendars were lunisolar and shared the same basic features of the other lunisolar calendars we've examined so far: twelve months, with a periodic intercalation of a thirteenth.
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).
The Hebrew calendar looks much like the Babylonian one, and there is clear influence from the time of the Babylonian captivity. In its earliest stage, the months were numbered, rather than named. The names eventually adopted were versions of the Babylonian names. As in Babylonian reckoning, Nisan was originally the first month of the year. Tishri became the first month along with the western part of the Selucid empire, and it remains so today.
Babylonian astronomy plays a critical role in the development of Greco-Roman astronomy, which is in turn essential for establishing a reliable chronology of the ancient world. Among other things, it is from the Babylonians that we derive our sexagesimal system for minutes and seconds. We are very fortunate that we are in a position to confirm independently the chronology found in major works like the Almagest. Thanks to excavations of numerous cuneiform tablets we have abundant evidence of the Babylonian calendar, the regnal dates of their rulers, and their astronomical observations.
No extant evidence is known that describes the workings of the oldest Egyptian calendar (that of the pre-dynastic period). We do know that it must have been lunar. Among other things, the hieroglyphic symbol for "month" shows a crescent moon (the first visible crescent of the new moon) over a star. Reconstruction of further detail has been attempted, but the argument remains controversial. Of greater interest for later chronology, particularly astronomical events, is the Egyptian civil calendar, whose existence seems certain by the fifth dynasty, and might, although the evidence is slender indeed, go back to the pre-dynastic period. There is also evidence for a much later, probably unconnected, lunar calendar. It does not, however seem to have been widely used. See Clagett and Parker for further details.
There are a variety of calendars that precede the one currently used in the west (the Gregorian) and which have some direct influence on it. Calendars that had no discernable impact (e.g., the Chinese, Indian, and Mayan calandars) are not discussed here.
Imagine yourself as an early astronomer. Your local ruler has been funding your research for several years, and now he wants some practical results. Your job: make a calendar. Which cycles are you going to include? What approximations are you going to make?
The following bibliography lists all sources consulted in preparing the article, as well as in compiling the feast days for the calendar applet. If you are interested in more detail about the general history of calendars and can read German, I strongly urge you to start with Ginzel, which despite its age remains indispensable. Another highly recommended work, which was published after I wrote the article, is Calendrical Calculations: The Millennium Edition, by Edward M. Reingold and Nachum Dershowitz (2001).
In principle, any astronomical cycle, e.g., the orbit of Venus or Mars, could be used to construct a calendar. In practice, very few societies bothered. These events were carefully recorded by astronomers, but only where these planets played an important role in religious observances (once again, see the Maya) were these events incorporated into the regular calendar.