The Golden Fleece originated when a Greek king named Athamas was about to sacrifice his son, Phrixus. Phrixus was hated by his step-mother, Ino, who plotted to have Phrixus killed and arranged for a fake oracle to call for Athamas to sacrifice Phrixus to save the kingdom.
Just as Athamas was about to sacrifice Phrixus, a winged ram with golden fleece appeared and prompted Phrixus (and also his sister Helle, who happened to be on the scene) to climb aboard. This golden-fleeced ram was sent by Phrixus' real mother, Nephele, to save her son.
Phrixus and his sister, aided by the golden-fleeced ram, flew away from Greece toward the East. Helle fell off the ram and the body of water where she died was named after her (the Hellespont). Phrixus survived the flight and landed at Colchis, on the southeastern shore of the Black Sea, where he sacrificed the ram to the gods.
The golden fleece was placed in a tree and it was guarded by a never-sleeping dragon (never-sleeping until it was eventually put to sleep by Medea, which allowed Jason to take the fleece).
For a detailed account of the story, see Apollodorus 1.9.1.