Although Sauron long knew that Men were easier to sway, he sought to bring the Elves into his service, as they were far more powerful. After the War of Wrath, Sauron decided that the Valar had forgotten about Middle-earth and he once again turned to evil.
After lying hidden and increasing his power in secret, Sauron put on a fair visage, calling himself Annatar, the Lord of Gifts, and in S.A. 1200 he befriended the Elvish smiths of Eregion, counseling them in arts and magic. He never came to Lindon as Elrond and Gil-galad did not trust him and refused to treat with him, although they never realized who he truly was. Elsewhere he was gladly received, especially in Eregion where the Elvish smiths learned much from him as their thirst for knowledge was great.
Under Sauron's tutelage the Gwaith-i-Mírdain, under the leadership of Celebrimbor, grandson of Fëanor, became more skilled than anyone else, save for Fëanor himself. In the year S.A. 1500, when they reached the very height of their power, the Elves began the forging of the Rings of Power, but Sauron knew all their secrets and in S.A. 1600 - ten years after the completion of the Rings of Power - Sauron created The One Ring to control the bearers of the other Rings.
But the Elves were not so easily ensnared, and as soon as Sauron put on the One Ring they and Celebrimbor were aware of him, and realized they were betrayed. They hid their Rings from Sauron and did not use them. Sauron demanded that the other Rings be given to him, for they would not have been without his knowledge. The Elves refused, and the War of the Elves and Sauron followed.