The Choshen Mishpat was a garment with a fold into which the Urim V'tumim were placed. Twelve precious stones or gems were embedded into the choshen, and the names of each of the tribes were engraved onto the stones. In addition, the words & אברהם, יצחק, שבטי ישורון, were also engraved, "spread" over all twelve stones. These names were placed on the Urim V'tumim to serve as a reminder of the great merit of our Avot and the tribes. The stones were arranged in four rows of three stones each, to remind us of the merit of the four Imahot. Between all the engraved words, every letter of the Hebrew alphabet is represented, allowing any word to be displayed by the lit up letters.
What exactly were the Urim V'tumim? Rashi states that the Urim V'tumim were scrolls of parchment on which Moshe wrote the 27 letter Divine Name. According to Rambam, there was more than one ineffable Name. Only Moshe could write this name, because he was the only man with the spiritual greatness required for writing this name. This is why the Urim V'tumim were not mentioned together with the other vestments and artifacts of the Mishkan which were contributed by artisans or the people. The Urim V'tumim caused the Choshen to light up and reveal answers to important inquiries. The word Urim means lit up, from the root אור. The word Tumim is translated to mean final and unalterable, from the root תמים. As opposed to the words of the prophets, which were not final but conditional (depending on the Teshuva of בני ישראל), the decision of the אורים ותומים was final and unalterable.
In the Torah's discussion of the Urim V'tumim, the Torah never tells Moshe to make them, as does with all other vessels and garments, rather it says ונתת אל חושן המשפט - that Moshe should place them into the חושן משפט. Why didn't the Torah say ועשית אורים ותומים as it says regarding the other Garments? This is telling us that the אורים ותומים was the work of heaven, and not the work of Man.
If a person had a question which needed to be resolved by means of the Urim V'tumim, he would go to the Kohen Gadol. The Kohen Gadol, would turn to the direction of the Aron, while the person would stand behind him and in a quiet voice (similar to someone who is praying) ask his question. The Kohen Gadol would meditate on the stones until he reached a level of Divine Inspiration. At that point he would be able to look at the letters that lit up on the Choshen and would be able to combine them correctly and decipher Hashem's reply.
Only matters concerning the king, the Bet Din, or the entire Am Yisrael could be resolved using the Urim V'tumim. It was not proper to inquire of the Urim V'tumim for private, practical purposes. Bnei Yisrael had used the Urim V'tumim throughout Tanach but they ceased to function after the destruction of the first בית המקדש . Josephus writes that the stones would shine at the end of a successful battle as a sign of victory. An ideal example of the use of the אורים ותומים was after Yehoshua's death, when some land in Israel still needed to be conquered. The question came up as to which tribe should go first into battle and conquer its land from the Canaanites. Pinchas, who was the Kohen Gadol at the time, entered the Mishkan and referred to the Urim V'tumim. The name Yehudah lit up, as did the letters י,ע,ל,ה. Pinchas had to figure out what these letters spelled. Ruach HaKodesh (Divine Insight) gave him the insight that they spelled יהודה יעלה, Yehudah shall go forth.
The Vilna Gaon gives a superb example of how the Urim V'tumim could be misunderstood. When Chana entered the Mishkan to pray for a child, the Kohen Gadol (Eli) saw her moving her lips in silent prayer. He consulted the Urim V"tumim about her, and the letters ש,כ,ר,ה lit up. When Eli saw this, he deemed Chana drunk, instead of deciphering the letters as כשרה, a worthy woman.
Aharon was the person who had been privileged to be chosen to wear the Urim V'tumim because of his happiness when he heard that his younger brother Moshe had been chosen to redeem Bnei Yisrael. Hashem therefore said: Let the heart that didn't feel jealousy wear the Choshen containing the Urim V'tumim.
During the final years of the first Bet Hamikdash, the prophet Yishayahu realized that Eretz Yisrael would soon be conquered, and the Kelim of the Mikdash would fall into profane hands. He removed the Urim V'tumim from the Choshen Mishpat and hid them along with the Aron containing the Luchot and the anointment oil. Ever since then, these items have been lost to the Jewish people. We pray for the day when they can be restored in a newly rebuilt בית המקדש.