According to the Babylonian Talmud (Yoma 73b) and the later commentaries such as Rashi, Maimonides and others, the Urim and Tumim worked as follows: .

Urim and Tumim , Rashi explains, refer to special names of G-d that were written and placed in the fold of the breastplate worn by the High Priest. In the fold of the breastplate were also 12 stones. The name of one of the 12 tribes was written upon each stone. According to the Talmud (Yoma 73b), in addition, the names of the patriarchs, Avraham, Yitzhak and Yaakov, and also the words "Shivtei Yeshurun" [tribes of Yeshurun] were also written on the stones in all 72 letters which included a complete alphabet.

When a question was brought before the Kohen Gadol , [High Priest] he would meditate on the Holy name of the Urim . This would cause some of the letters on the stones of the breastplate to protrude. These letters formed the answer to the question. However, since the letters were not in any special order, the Kohen Gadol would then meditate on the Holy name of the Tumim and in so doing  would receive Divine inspiration as to how to arrange the letters properly and thus answer the question.

I hope this answers your question.