The Mayans did not have any complex instruments for charting the positions of celestial objects, so their observations were with the naked eye. They may have used rudimentary instruments, such as crossed sticks to chart position, but they lacked the armillary spheres or sextants of other civilizations.
However, the Mayans were excellent builders and many of their temples and buildings are aligned to help observers monitor position. For example, many buildings pointed towards the equinoxes or midsummer, whilst other buildings had doorways and windows aligned with the most northerly or southerly rising of Venus, one of the most important celestial bodies to the Mayan culture. So accurate were their observations that their predictions of the orbit of Venus lost only two hours in a 584-day cycle.