In the historic era (the era of written records, as opposed to prehistory), absolutely chronology is determined by first establishing a relative chronology until a benchmark event can be established.

In other words, contemporary chroniclers (people writing the events of their day) usually describe an event in relation to others, e.g. X happened 4 months after Z came to power on the first moon after the winter solstice, or, as in Greek antiquity, Y happened in the second year of the 14th Olympiad. And since we know when the first Olympiad was (776 BCE), we go from there.

Calendars themselves are generally reliable in the historic era. We can calculate lunar and solar dates easily. But sometimes we get conflicting accounts from ancient historians as to specific days. In those cases, modern historians try to determine the more credible ancient source based on other chronological and historiographical criteria.

All that said, determining absolute chronology is not all that important to most historians, beyond what has already been done, that is. It was more important to modernist-era historians, and now we can ask other questions.