James Hunt says that Joseph translated the BOM with "the big spectacles," the biblical Urim and Thummim, and by looking into his hat.
James Henry Hunt, Mormonism: Embracing the Origin, Rise and Progress of the Sect (St. Louis: UStick & Davies 1844), 13-14
Another account given of the transactions is, it was translated with the big spectacles, before mentioned, which were in fact the identical Urim and Thummim mentioned in Exodus xxviii. 30, which were brought away by the heroes of the book from Jerusalem, handed down from one generation to another, and finally "hid up unto the Lord," in Ontario county, New York, some fifteen centuries since, to enable Joe to translate the plates without looking at them! . . . [I]n a few weeks, Harris made his appearance, and soon Cowdery was in attendance, and Joe again commenced looking into his hat and telling of his bible.