It depends a great deal upon where they were. A calendar dating system really is just a an agreed on method of picking a reference date and starting from there.

For most cultures, that involved the regnal years of monarchs. Egyptian dates, for instance, are usually given as a number of years into the reign of a Pharaoh. The Romans usually referred to the year by the names of the two consuls who were serving that year. In your case, the year 20 BC would have been the year of the consulship of Marcus Appuleius and Publius Silius Nerva.

The Romans also had a dating system, with its year one denoting the traditional founding of Rome and corresponding with our year 753 BC. This dating method was used by some Roman historians, but the consular dates were more likely to be used in day to day situations.

Other cultures had their own dating system, based on their own criteria. The Jews use a calendar which places Year 1 as one year before the creation of the world, calculated as 3761 BC (although prior to the 12 century, the reference date was the destruction of the first Temple).

Dating from the birth of Christ didn't start until the 8th century, when the Venerable Bede used that system for dates in his "Ecclesiastical History of the English People". His year 1 was based on the calculations of a monk named Dionysius.

So not only would you not have known that 20 BC was 20 BC if you had lived then, you wouldn't have known that AD 20 was AD 20 either.

The current system was not in widespread use in Europe until after the eighth century, following which it became increasingly popular. Prior to this, and in many areas even after this, you would likely have referred to yourself as being in the 10th year of the Kings reign for instance.

One oddity is that we use a slightly different calendar system now than was used then. For many years, the Julian calendar was in use. In the 1500s, Pope Gregory established a slightly different calendar system which bears his name. It was done due to some increasing accuracy in the way that the church calculated the date that Easter falls on every year.

The major difference is in the placement of leap years and the lengths of months. When the Gregorian calendar was approved, something a little odd happened. At that point, the Julian calendar and the Gregorian calendar were about 12 days off. So everyone who adopted the new calendar suddenly found themselves 12 days in the future in a sense. This led to some confusion as there were areas that have not adopted the new calendar, and were still going by the old dates. You could travel from one town to the next, and find yourself 12 days in the past or in the future.

Although the Gregorian calendar was primarily developed for religious purposes it gradually came into use for civil purposes as well, including in non-Christian areas of the world. Today it is the generally excepted calendar for the vast majority of the world.

The Julian calendar is still in official use by the various branches of Orthodox christianity. This is why orthodox Easter falls on a different date than the one that is used by Catholics and other Christians.