Obviously we think of this year as 2014 AD. How did people distinguish the years before we started using this scale? Did they simply not have a need for year counting? Has there been anything found in Egyptian hieroglyphs or some lost scroll from the middle ages that determines those people were using year counting?
Nitpicky, but there was no year 0 in the AD/BC system. 1 AD was the year after 1 BC. Also, the AD/BC system didn't really take off until after it was popularised by the Venerable Bede around the early 8th century AD.
As /u/th3_rhin0 mentions, one way was to say who held office in that year. This is what the ancient Greeks often did: in the archonship of so-and-so, for example. The Romans had a few ways: in the Roman republic they would date by the two consuls of that year, and in the imperial period they often use the emperor's various titles and positions (which consulship he was holding at the time, how many times he had been granted tribunician powers, how many times he'd been hailed "imperator"). Alternatively, they counted years ab urbe condita, from the founding of the city.
There were different ways ancient civilizations marked the passage of years. In agrarian societies time was kept by season, (flood season, planting season, harvest,... Etc.). One could say that a major event occurred x number of harvests ago. This was fairly easy since these events generally occur at the same time every year.
Another, more common in later civilizations, method was keeping years by who held public office. The Romans marked time by who held the consulship - saying that some event occurred in the consulship of whoever.
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In addition to what others have said, you may also want to check out Episode 6 of the AskHistorians Podcast!
Romans often referred to years by the consuls reigning during the Roman Republic. Eventually, later in the life of the Republic, dates were given based on the legendary founding of Rome (753 B.C. is usually the given date for this)
To expand on /u/th3_rhin0's response, the Romans indeed dated by the year's consuls and this practice was adopted in many areas they conquered and incorporated into their empire. Local dating practices endured, however, either instead of consular dating or in conjunction with it. For a particularly intricate example, see this papyrus document (text) in Greek and Aramaic from the archive of Babatha, a Jewish woman from the village of Maoza in the Roman province of Arabia.
The document begins as follows:
"In the fourteenth year of Imperator Traianus Hadrianus Caesar Augustus, in the consulship of Marcus Flavius Aper and Quintus Fabius Catullinus, three days before the Ides of September, (but) according to the reckoning of the new province of Arabia, in the twenty-fifth year on the twenty-fourth of Gorpiaios..."
The year of the document is thus indicated by 1) the regnal year of the reigning emperor 2) the consuls and the Roman month 3) the number of years since Arabia became a Roman province and the Macedonian month (introduced long before when Arabia was a part of the Seleukid empire). It was written on Sept. 11, 130 CE by our calendar.
In China, the main way up until 140 BCE was through the counting of the years a ruler was on the throne. The Chunqiu Zuozhuan goes by such dates as "the eighth year of Duke Xi of Lu" or "the fourteenth year of Duke Cheng of Lu." In 140 CE, the Emperor Wu of the Han Dynasty instituted the era name system, where a certain set of years would be one named era. This system was used until 1911 in China. So for example the years 32-28 BCE became the era of Jianshi, so 30 BCE would be the "the third year of Jianshi." Japan eventually issued its era name, and continues to do so today. This year is the 26th year of Heisei under this system. Korea either adopted Chinese era names, except for a few very rare times when it issued its own era names (as was the case before the 1910 annexation by Japan), or marked years by the year since the ruler had acceded to the throne.
There is also another system in all three countries, the sexagenary cycle, where each year for sixty years has a certain name, and then the cycle starts over again. This lunar year, 2014-2015, is the Jiawu year. Since it repeats every sixty years, a reference to Jiawu could be to 2014, 1954, 1894, etc. This is usually a problem with ancient history, not modern history.