What can be said about the historical sky cult rests on a thin but real body of evidence, and it is worth being clear about what that evidence is.
The central texts are the Old Turkic inscriptions raised in the Orkhon valley of present-day Mongolia in the 730s, commemorating the Gokturk prince Kul Tigin and his brother Bilge Khagan. They are the earliest substantial writing in a Turkic language, and they invoke Tengri repeatedly and matter-of-factly: heaven above and the dark earth below, the Turkic people made between them, and the khagan raised to rule because Tengri willed it. Defeat is explained the same way, as Tengri withdrawing favour when the people failed. Alongside Tengri appears Umay, associated with the womb, birth and the protection of children, and the sacred earth and water, yer-sub.
The same complex reappears in the Mongol empire several centuries later. Chinggis Khan and his successors justified their authority by the mandate of eternal heaven, a formula that opens Mongol letters to foreign rulers; the phrase is on the imperial seal impressed on the letter Guyug Khan sent to the pope in 1246. Friars and envoys who reached the Mongol court, William of Rubruck among them, describe rites, diviners and a broad tolerance of other religions consistent with that framing.
Chinese sources record comparable sky worship among earlier steppe peoples including the Xiongnu, though what they preserve is filtered through Chinese categories.
What is not in the record matters as much. There is no scripture, no clergy hierarchy, no creed, no fixed pantheon, and no name for the system used by its own practitioners: "Tengrism" is a modern coinage. The sky cult coexisted with ancestor rites, cults of mountains, rivers and fire, and with ritual specialists, and it was an aristocratic and political religion above all: the sky legitimated rule.