Roman dates are given by using references to three sacred days which fall at roughly the same time each month. These days are the Kalends, the Nones, and the Ides. These will be returned to again, shortly.
Dates are given by counting, inclusively, backwards from the next reference day, putting this number, ordinally, in the accusative case, after the words "ante diem," excepting one case, which is the day before the referenced day, in which case rather than the number and "ante diem," the word "pridie" is used instead. Usually, instead of writing each word out, the words "ante diem" are abbreviated to "a.d.," "pridie" is abbreviated to "pr.," and the number is just given as a numeral. Following this, the referenced sacred day and month is placed in the feminine accusative plural.
The Kalends ("Kalendae", in Latin; abbr. "Kal.") always fall on the first day of the month. The Nones (Nonae, "Non.") fall mostly on the 5th, but on the 7th in March, May, July, and October). The Ides (Idus, "Id.") fall mostly on the 13th, but on the 15th in those months just referenced.
Therefore, to reference the 29th of January, for instance, the date would be "ante diem quartum Kalendas Februarias (a.d. IV Kal. Feb.)," literally translated to "the fourth day before the February Kalends (usually reckoned as "Kalends of 'month'"). Similarly, the 14th of March: "pridie Idus Martias (pr. Id. Mar.)," i.e., "the day before the March Ides."
But, there is an exception. When the date to be give in one of these three sacred days (Kalends, Nones, Ides), the date is given as strictly the day and month, both in the feminine ablative plural. Therefore, "Kalendis Aprilibus," "Nonis Septembribus," "Idibus Maiis."
Years are given in one of two ways: either with reference to the year's consuls, or with reference to the year of the founding of the City. When using the former reference, the names of both consuls are given in the ablative case, followed by the word "consulibus (cos.)." So, 63 BCE would be "M. Tullio Cicerone et C. Antonio Hibrida consulibus." Also, it was not uncommon to shorten this simply to the cognomina of the two consuls, so the previous would be "Cicerone et Hibrida cos." When using reference to the founding of the City (i.e., Rome), the accepted date is 753 BCE, which would make the year 2001, for instance, "2754." This number is given, followed by the words "anno Urbis conditae" or "ab Urbe condita" ("in the year of the founding of the City" or "from the City being Founded"), both abbreviated "a.u.c."