Mayan Astronomy

Unlike the ancient Celts who measured time with respect to the night, the ancient Maya were more interested in studying the sun.  This is probably a consequence of their beliefs, which include a sun god, Kinich Ahau, but no lunar deity.  That's not to say that they completely ignored the moon, because they eventually started tracking the lunar cycle, but it wasn't their primary concern.

Predating the Coligny Calendar by a few thousand years, the (in)famous "Mayan Calendar" is actually a system of calendars.  We know about their calendars because before the fall of Mayan civilization, they, again unlike the ancient Celts, left behind a lot of written pieces documenting their work.  There are four such pieces, known as the Dresden, Madrid, Paris, and Grolier Codices.

The Dresden Codex is in the best condition of all the codices.  Its most well-known contents are the accurate calculations of the lunar cycle, including predictions of eclipses, and descriptions of the motion of the planet Venus.  One of their many calendars was based on the movements of Venus.  It was 260 days long, which is the amount of time Venus is seen in the morning and, 50 days later, in the evening.  This Venus calendar ran concurrently with the 365-day calendar marking the solar year and the lunar calendar that kept track of the lunar cycle.

From the Wikipedia page on the Dresden Codex

The Madrid and Paris Codices mostly contain information about the Maya religious deities and rituals.  They document the constellations and what they meant to the Maya, describing the ceremonies done by priests at different times of the year.  The existence of the fourth codex is under some scrutiny because it's the least intact and contains simple descriptions of the Venus motion described in the Dresden Codex.  

The ancient Maya were able to to find such accurate measurements not because they had advanced technology*, but because they recorded careful observations over hundreds of years.  That was the method used by all ancient civilizations interested in astronomy.  

*They did have a really cool observation setup that resembled our modern inferometry.  They spaced out their temples in such a way that they could observe objects in the sky from different angles and get a more complete view of the same celestial object.  

From authenticmaya.com