The actual Roman year was normally specified in one of two ways:
In ancient Rome in the time from the Republic (as soon as Tarquinius Superbus was thrown out) to the start of the Imperium Romanum (after the murder of Caesar and Octavianus's 'election' to Supreme Ruler of the Empire) the year was specified simply by listing the consules that were elected for that particular year. Thus 63 BC would be M Tullio C Antonio consulibus1.
Ab Urbe Condita
Another way of specifying the current date was to give the number of years elapsed (counting inclusively) since the city (Rome) was founded - an event that according to the legend and the great Roman historians occurred in the year 753 BC.
Thus 63 BC would be 691 ab urbe condita, also written as 691 a.u.c. or DCXCI a.u.c. or Anno DCXCI a.u.c., and read out as Anno sescentesimo nonagesimo primo ab urbe condita.
Hereby, all numbers are ordinals ie, the Roman equivalent to first, second, third...
After approximately 500 AD, what was left of the Roman Empire started using dates originating from the birth of Christ - Anno sexagesimo tertio ante Christum natum or anno LXIII a.Chr.n..
When it comes to specifying exactly which day we are talking about, things tend to get a bit messy. To begin with, there are two different calendars. Before 45 BC, a year was only 355 days long, and thus they kept inserting leap months every now and then. After Caesar's reformation, the year was long enough for itself, and we got rid of things like June in the winter, and so on.
Four of the months were special - they had before the Julian calendar 31 days: March, May, July and October (Martius, Maius, Quintilis, October). February (Febrarius) had 28 days and all the rest 29 days. Caesar increased the number of days in January, August and December (Ianuarius, Sextilis, December) with two days to 31 days, and April, June, September and November with one day to 30 days.
All in all, the Roman year started with March and numbered certain months after assorted deities, and the rest simply numerically (September = the seventh month):
The Romans based all their dating on three main days in each month: Kalends, Nonae, Idus (plural words). Kalends was the first day of each month, Nonae was the fifth day (in March, May, July and August the seventh) and Idus the 13th (15th) day2.
On the actual day, the date is given with a temporal ablative: Idibus Martiis (15 March).
The day before was pridie, and the day after, postridie, and together with one of these, the day is expressed in the accusative: pridie Kalendas Ianuarias (29 December or after the reformation, 31 December) or postridie Kal. Ian. (2 January).
All other days are expressed counting down towards the next main day, inclusively (ie, count both today and the main day); thus decimo Kalendas Apriles (with separative ablative for decimo) (23 March).
Commonly, the term ante diem (before the day) was used with accusative in the number instead of the ablative, thus: AD X Kal. Apr. or ante diem decimum Kalendas Apriles.