How did the Mayans develop their calendar by tracking Venus in the sky?

It would be accurate to say that the ancient Maya of Central America, who had no telescopes, did not measure Venus itself but kept careful records of its apparent track in the sky.

Because of the relative orbits of Earth and Venus, Venus is first invisible, then appears in the morning sky, then disappears, then reappears in the evening sky, then fades from view again.

An important part of the complex Mayan calendrical system is based on the 584 days it takes for Venus to make that complete cycle.

The Venus cycle was meshed with a sacred calendar of 260 days and the 365-day solar calendar to come up with a cycle of about 2,920 days, or 8 solar years, in which the calendars came out approximately even.