Around S.A. 1200, Sauron started to corrupt the Elves. He did not manage to approach Gil-galad and Elrond but had better luck with the Elven-smiths of Eregion. The Gwaith-i-Mírdain of Eregion were mostly Noldor, and wished to have the same joys in Middle-earth as the Elves who had returned to Valinor. Sauron presented himself as "Annatar", an emissary from the Valar, and tempted them by offering knowledge to transform Middle-earth.
Annatar taught the smiths knowledge of how to create Rings, which would grant the Elves who wear them certain powers. About S.A. 1500, the great sixteen were created.
When Annatar departed from Eregion, Celebrimbor went on to forge the Three Rings using knowledge he had gained, but without his involvement.
Sauron then created the One Ring around 1600, alone, in the heart of Mount Doom. Its purpose was to rule over all the other rings, and Sauron put a great part of his power into it. The Elves heard him speak the spell, and realized they had been betrayed.