Say there was to be a gladiator fight on the 16^th of July in 100 AD and some slave would want to create some hype for this.
How would he write down the date? In roman numerals, but would the format be DDMMYYYY or MMDDYYYY or something completly different? Did they distinguish between AD and BC? How? Did they use a different calendar and how would that impact this? Is it even possible to convert modern dates to ones that would be understood by Ancient Romans?
The roman calendar used three reference dates (Kalends, Nones, and Ides) and referred to dates by counting backwards from the next reference date. The Kalends were the first of the month, the Nones were the 5th or 7th, and the Ides were the 13th or 15th.
On the first of the month, you'd say it was the Kalends, then the next day would be the "fourth day before the Nones" and so on until you reached the Nones, then "so many days before the Ides", then the Ides, and finally "So many days before the Kalends" until the month rolls around. In latin, these dates would be expressed as "Ante Diem III Nones November" (three days before the nones of november, or November 2nd) and the common short hand writing was ad III non. Nov.
The dates for the Nones and Ides moved depending on the length of the month, which were 29 or 31 days long. Short months had the Nones on the 5th and the Ides on the 13th, while long months used the 7th and 15th. Well, there was also February, which had 28 days. It used the same naming convention as short months.
Today's date would be twelve days before the Kalends of November October. (Thanks to SiliconGuy for the correction) or ad XII Kal. Oct.
July 16th would be 15 days before the Kalends of Sextilis. (August)
Years were a little less set in stone. During the republic, years were named after the consuls, who served one year terms; later the convention of counting from the founding of the city was used. So AD 100 would be the 853 year since the founding of the city, ab urbe condita, abbreviated AUC.
Source: Ecce Romani 3rd edition.