The Roman Republican Calendar
There were 12 months in an ordinary year, but many of the months were shorter than they are now (see the Julian reform). Their Latin names will largely look familiar. A regular year thus had 355 days. The lengths of the months indicate that by the time of our earliest records the year was not measured by direct observation, as no month so measured could have 31 days, but by conventional rule.
The number-names of the last six months indicate not, as is sometimes said, that there were originally 10 months (a number that if true would yield a nonsensical year length), but that the year originally began in March. There is a fair amount of confusion in different accounts of the Roman calendar about the beginning of the year. Sometimes it will be said that the year began on March 1 until Julius Caesar reformed the calendar. This theory was disproved by the excavation of an actual republican calendar in the 1920s, which clearly shows the year started in January. It is also sometimes said that the beginning of the year changed in 153 BCE, but in fact what happened this year was that the time when consuls took office was synchronized with the calendar year. January seems to have become the beginning of the year when the republican calendar was introduced, but there is so little information about that reform (taking place, it appears, in the 5th-century BCE) that we can say little more.
To keep the calendar roughly in line with the seasons, a leap month (it had no name other than "the intercalary month") was inserted at the end of February. This position, which falls more or less at the end of the year when the year began in March, implies that the intercalary month predates the change in observation of the new year. The decision to insert the intercalary month was made by the pontifexes. In theory the intercalation was roughly every other year. In practice, pontifexes seem to have been rather lackadaisical in carrying out their offices, and the calendar was sometimes allowed to get drastically out of synchronization with the seasons. Roman intercalation was peculiar. February was reduced to either 23 or 24 (it varied from year to year), and a 28-day month was added afterwards. This peculiar habit was a result of the ways that days of the month were counted in the Roman system.
There were two important festivals, Refugium and Equirria, which fell at the end of February and which could not be separated from the beginning of March. They are transferred to the intercalary month, but notice with the Roman method of counting backwards, they keep their day numbering constant whether it's a regular or intercalary year. Note that our general conversion rule applies for intercalary years as well. If February has 23 days, February 15 = a. d. x Kal. intercal. (xi if Feb. has 24).
The Roman calendar also had a recurring cycle of 8-days, similar to our week, called the nundinae = nine-days (once again, we have that habit of inclusive counting). This "week" was not religious in significance, but originally indicated days upon which a market would be held in Rome. Extant Roman calendars indicate this interval by giving each consecutive day a letter A through H. Note that this was simply a mnemonic marker. They did not call them "day A," etc. The 7-day week and its names were not introduced into Roman civil life until the imperial period.
While dating by Olympiad was occasionally used, Roman writers most often reckoned years by the eponymous names of the consuls in office that year. This habit persisted through the imperial period as well, even though (excepting those occasions when the emperor was also consul), consular power was much reduced. An unbroken list of consuls from the founding of the republic (conventionally, 509 BCE) through the late empire survives. Some have questioned whether all the earliest names in this are historical, but the later ones certainly are, and provide many opportunities for correlation to the Common Era.
The so-called Varronic Era, named for the late Republican antiquarian Marcus Terentius Varro, was only rarely used during the Republic, but became more popular under the emperors. In it, years were dated from the founding of Rome, or AUC (ab urbe condita), which was correlated to the Greek reckoning by saying that it fell in Olympiad 6,3 (olympiadis sextae anno tertio), i.e., 753 BCE. Like most eras calculated from a foundational date in the distant past, the Varronic Era should be seen as purely conventional. That is, even if Rome wasn't founded in 753 BCE, dating in this system can still work just fine, as long as it remains consistent.