They asked Zeus who was the fairest. Zeus reluctant to be the judge, told them to present themselves before Paris who was an excellent judge of beauty.
... And they each made a bribe to Paris, Hera offered dominion of Asia and Europe... Athena offered a glorious military career with skill and wisdom and Aphrodite offered the love of the most beautiful women in the world, Helen.
Paris, a weakling and something coward , too, as later events showed, chose the last. He gave Aphrodite the golden apple.