The original Roman calendar was assumedly borrowed, in part, from the culturally advanced Greeks. Unfortunately, this early calendar was based on 10 months and only 304 days. The remaining 61 days that were later discovered to have been missing, were basically ignored and just occurred sometime during the winter season. The 10 months, beginning in modern March, were named Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November, and December. The last six of these months were derivatives from the Latin words for five, six, seven, eight, nine, and ten, respectively. According to legend, Romulus, the fist King of Rome, is supposed to have introduced this calendar in the 8th century BC.
A following king, Numa Pompilius, is accredited with the addition of Januarius and Februarius, as winter months, to the calendar. Other reforms are often attributed to the Etruscan King Tarquinius Priscus, who ruled between 616 and 579 BC. These additions and the rest of the calendar were months, however, were still based on a lunar cycle, making the Roman year 355 days long. The ancient astronomers did have at least limited knowledge of the Solar year and periodic adjustments were made to bring the calendar in line with the appropriate season. Every other year a month called Mercedinus was inserted after February (March was the beginning of the year) adding an additional 23 or 24 days to the year. Mercedinus, which translates as payment for work was the time when property lessees paid rents due to their landlords.
Later in the Republic, Mercedinus gradually became known as Intercalans and could have variable lengths to right the seasons to the weather. It simply meant an inserted length of time into the calendar. It was the duty of the Pontifex Maximus to decide when and how long an Intercalans would be implemented.
The Romans referred to years in a couple of ways. Each year was recorded as a length of time from the traditional founding of Rome, in 753 BC. The Latin term Ab Urbe Condita, abbreviated as AUC, literally meaning from the founding of the city, was the correct terminology. Additionally, years could be referred to as the year in which a particular Consul was in office. As examples, the modern year 59 BC, would've been known as 694 AUC, or the year of the first consulship of Gaius Julius Caesar.
Three days were structured with particular importance in the Roman calendar. The periods in between these intervals were of various lengths and days were counted backwards to the appropriate major day. For example, as the Calends was the first day of the month, March 23rd would be referred to as 9 days before the Calends of April.
Calends (or Kalends) - Occurred on the first day of every month and it had more days than the other two period combined. It spanned more than two lunar phases, starting from the day after a full moon and continuing through the moon's last quarter and waning period, then past the dark new moon until another lunar crescent was sighted. The day of Kalends began a new month. It was dedicated to the god Juno.
Ides - Occurred on the 15th day of every month which contained 31 days, and the 13th day of all other months. Ides was dedicated to Jupiter and was originally based on the date of a full moon. Because a full moon occurs halfway thru each lunar cycle, its day was called "Idus" from the Latin word meaning to divide. The next new moon was expected to develop between 15 to 17 days. Variations in this length of time, due to the lunar and solar cycles not corresponding exactly, led to Ides becoming mainly a day marking the middle of the month.
Nones - Always occured nine days before the Ides, on either the 5th or 7th of the month, depending on the length of the month. It was representative of the moon reaching its first quarter phase. As it was the duty of the Pontifex Maximus to assign these days, he would, after viewing the moon, assign how long it would take for the next phase to begin. If, on the day after the Kalends, he determined that it would be 5 days until the new crescent moon would appear, the day would then be referred to as the 5th day before Nones.