What happened in the first beauty contest among the gods?

Just before the Trojan war, the apple of discord (a golden apple that was especially beautiful) was thrown among the goddesses. On it was written “For the fairest.” Among all the goddesses, three were chosen as especially beautiful-Aphrodite, Athena, and Hera. The goddesses asked Zeus to decide between them, but he wisely demurred. Paris, a mortal prince, was chosen to make the final decision. All three goddesses tried to bribe him to choose her. Aphrodite offered him the most beautiful woman in the world-Helen of Troy. Athena offered him prowess in battle. Hera offered to make him the great king of the earth.

Paris chose Aphrodite.

According to Homer, this was the major cause of the Trojan war, because Helen’s husband wasn’t very happy when Aphrodite helped Paris kidnap Helen. He pursued her and the rest is history.