How did people in ancient times display their years in their calendar, I highly doubt that Ancient Rome's calendar read 180 B.C.?

Wherever we turn up records and artifacts, we usually discover that in every culture, some people were preoccupied with measuring and recording the passage of time. Five thousand years ago, Sumerians in the Tigris-Euphrates valley in today's Iraq had a calendar that divided the year into 30 day months, divided the day into 12 periods, and divided these periods into 30 parts. We have no written records of Stonehenge, built over 4000 years ago in England, but its alignments show its purposes apparently included the determination of seasonal or celestial events, such as lunar eclipses, solstices and so on.

The earliest Egyptian calendar was based on the moon's cycles, but later the Egyptians realized that the "Dog Star" in Canis Major, which we call Sirius, rose next to the sun every 365 days, about when the annual inundation of the Nile began. Based on this knowledge, they devised a 365 day calendar that seems to have begun around 3100 BCE (Before the Common Era), which seems to be one of the earliest years recorded in history.

Before 2000 BCE, the Babylonians (in today's Iraq) used a year of 12 alternating 29 day and 30 day lunar months, giving a 354 day year. The Mayans of Central America relied not only on the Sun and Moon, but also the planet Venus, to establish 260 day and 365 day calendars. This culture and its related predecessors spread across Central America between 2600 BCE and 1500 CE, reaching their apex between 250 and 900 CE. They left celestial-cycle records indicating their belief that the creation of the world occurred in 3114 BCE. Their calendars later became portions of the great Aztec calendar stones. Our present civilization has adopted a 365 day solar calendar with a leap year occurring every fourth year (except century years not evenly divisible by 400).

http://inventors.about.com/library/weekly/aa070701a.htm

Different civilizations used different epochs (i.e. important events) as reference points for the beginnings of eras.

For the Romans, the epoch was usually the foundation of the city, which they reckoned to be in the year that we call 753 BC/BCE. So 180BC/BCE would have been the 574th year from the foundation of the city (AUC DLXXIV: anno urbis conditae quingentesimo septuagesimo quarto). They also identified years by reference to the consuls who held office, making 180 BC/BCE the year of the consulship of Postumus Albinus Lucus and Gaius Calpurnius Piso, but this must have been very inconvenient.

The Greeks went back to the first Olympic Games, held in 776 BC/BCE, and reckoned by Olympiads. An Olympiad was the period of four years between Games. So the year running from approximately the summer solstice in 180 BC/BCE to the solstice of 179 BC/BCE would have been the first year of the 150th Olympiad (I think). This system seems to date from the third century BC/BCE: before that different systems were used in different cities.

In Europe, although the Christian era gradually came to prevail during the Middle Ages, the use of BC for years before the birth of Christ is much more recent. Medieval and Renaissance historians would sometimes use the supposed creation of the world in about 4000 BC/BCE as an epoch.

As to what the calendars must have looked like, rather than how they worked:

The only unit of time that was larger than a year was the reign of a king. The usual custom of dating by reign was: "year 1, 2, 3 . . . , etc., of King So-and-So," and with each new king the counting reverted back to year One. King lists recorded consecutive rulers and the total years of their respective reigns. The civil year was divided into three seasons, commonly translated: Inundation, when the Nile overflowed the agricultural land; Going Forth, the time of planting when the Nile returned to its bed; and Deficiency, the time of low water and harvest.

The months of the civil calendar were numbered according to their respective seasons and were not listed by any particular name–e.g. third month of Inundation–but for religious purposes the months had names. How early these names were employed in the later lunar calendar is obscure. The days in the civil calendar were also indicated by number and listed according to their respective months. Thus a full civil date would be: "Regnal year 1, fourth month of Inundation, day 5, under the majesty of King So-and-So."

http://webexhibits.org/calendars/calendar-ancient.html