The Romans had a Calendar, from memory it had 10 months, some of it remains in our modern calendar (oct = eight, Nov = nine, Dec = 10).
Julius Cesar added a month, hence July, Augustus Cesar added a month hence August.
I would imagine there is a way to convert from the old Roman calendar to the modern one, so they can work out the years.
The Romans wouldn't have counted based on BC/AD, later writers would have done that.