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Observation is the name of the game.
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"You can see a lot by looking."
-Yogi Berra
Not having any of today's distractions and nearly zero light pollution, it wasn't all that hard for various cultures to figure out the basics of astronomy. Mostly, it came from some sort of record keeping of what the sky looked like when a particular event occurred - Such as when the star Sirius appeared on the eastern horizon at dawn, then the Nile was expected to flood. Or when the Sun reach solstice or equinox.
Tie stuff like that into religious and cultural events and you have a handy way of marking out the calendar. Make stories out the the groupings of stars and monitor the path of the planets, and you can scam people into astrology.
After awhile, smart folks can figure out the math of when an object will appear in the future, like the saros cycle of solar eclipses.
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Ancient Chinese observed Crab Super Nova.
Observation, deduction and imagination, all were used in ancient astronomy.
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They had brains, eyes, dark skies, and lots of time.
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Ancient civilizations were much more advanced that we think.And in that time there was an open alien activity on Earth.
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Studied the patterns in the sky. Associated same with seasons.
When star A is between peak b and peak c, get ready for snow.
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They studied the sky - you don't need a plane or telescope to see the stars and watch their movements.
Some astronomers kept detailed observation notes of when the stars rose and set, when the planets were visible, the phases of the moon.
Why is that so hard to understand? Yes, because they had eyes and the skies were dark - seriously.
What do you expect us to tell you? Before modern society, there was no light pollution to dim the stars, and no TV or internet to entertain people and keep them inside and keep them uneducated like kids today.