[Lord Starshadow]

The Elves and Sauron exchaged a lot of information during the time of the forging of the Rings of Power, and they thought him a friend for quite a while. Sauron learned the craft of ring-forging from the Elves, and he aided their creation of the Nine, which were given to Humans (who became the Nazgul), and the Seven, for the Dwarves (you may remember Gandalf mentioning trying to retrieve it from Thorin's father and of Balin's attempt to re-enter Moria). So while Sauron did not have a hand in the making of the Three, he was well-versed in their craft and so was able to create the One Ring. He did have to put a lot of his power into the making, and that's why he wants it so much.