While there is no description as to the Urim and Thummim's form, it has been theorized that they are two dissimilar stones which can be distinguished from one another by their color, type of stone, or words which have been engraved upon them (1 Samuel 28:6).
Again, while the precise manner in which to operate the Urim and Thummim is largely unknown it has been theorized that the Urim (a white stone) represents 'no'; while Thummim (a black stone) represent yes. To use the stones, they are placed in a bag, a objective question is asked and a stone is drawn unseen from the bag.
It is interesting to note that the ancient Hebrews believed in only three forms of communication with God. They are through dreams, through prophets, and through Urim and Thummim. This would make Urim and Thummim the only form of divination sanctioned by the Judiasm, and therefore God.
As someone who's ancestry is, in part, Jewish I was once very interested in the ancient beliefs of the Jews. As such I collected my own set of Urim and Thummim. These stones were cleansed by wiping them down with ammonia and anointed with a combination of Psychic Vision Oil, King Solomon Oil, and High John the Conqueror Root oil and prayed over in the name of God.