The warrior Bellerophon spotted the majestic steed grazing at a Corinthian spring and tamed him with the help of a golden bridle supplied by Athena. Pegasus proved a loyal companion to the ambitious hero through many adventures. Unfortunately Bellerophon, lacking good horse sense, invited himself to Mt. Olympus. In some versions Pegasus bucked him off as they were winging their way to the gods' territory. In others the horse jumped when stung by a hornet sent by Zeus, unseating Bellerophon who fell to earth.
In either case, Bellerophon was doomed to remain earthbound while Pegasus was welcomed to Mt. Olympus where he served the gods as faithfully as he had Bellerophon before hubris and horse unseated him.
Do you hear his hoofbeats in the thunderstorm? He's fetching thunderbolts for Zeus. He is sometimes asked to carry the goddess Eos (Aurora) as she brings in the dawn. At other times Apollo rides him as he leads the sun across the daytime sky.
Pegasus is among the constellations listed by Ptolemy in the 2nd century. In the Northern Hemisphere October is said to be the best month for viewing Pegasus.
The Houston Astronomical Society has a helpful explanation of how to locate the constellation Pegasus.