First you start with observations. People watched the skies for centuries, out of both boredom and religious intent. They meticulously recorded events.

After a while it became apparent that major events weren’t simply random - solar and lunar eclipses seemed to come in clumps, and always correlated with full or new moons.

With enough data on this, medieval astronomers could start to work out the mathematics behind it - the Earth and the Moon have very predictable orbits and will repeat the same cycles over and over again.

Today the orbits are well modeled, and we can predict eclipses with extremely high accuracy.