The Elven-smiths of Eregion began making the Rings of Power, see Appendix B c. 1500 for example. The Dwarves of Durin's folk said that the first of the Seven to be forged was given to Durin III by the Elvensmiths themselves, not by Sauron...
... but Of The Rings Of Power And The Third Age relates, concerning Sauron (who came with war to Eregion): 'Seven rings he gave to the Dwarves; but to Men he gave nine,...'
I tend to believe this a bit more than the Dwarvish version :)
Another account reveals only that Celebrimbor, under torment, revealed where the Seven were bestowed. This detail is from a roughly composed outline, not published by Tolkien himself -- though JRRT himself did not publish Of The Rings Of Power as well, and plenty of other texts now in print, in any case.