Now, we see from Sauron's appearance among the Elves of Eregion as Annatar, that he came as a "Teacher" and a "Lord of Gifts" supplying secret knowledge by which the Elves were able to combine their own lore and create the Great Rings. Therefore it is an easy jump to assume that Curunir, being also from Aule's people, already had a great store of "once secret" knowledge of his own... enough to at least begin the trials of ring making. His only missing element should have been the discoveries of Celebrimbor and the Smith's of Hollin.
While much had perished in the Wars of the RIng, not all had been lost, as the point continues to prove itself. My own belief is that he attained enough knowledge from secret scrolls and the minds of the Elven ring-wearers to make a serious attempt at a Ring of Power. Because, like Sauron, the greater part of the knowledge to do this seems likely to have already been his.