(30) Inside the breastpiece of judgement you shall place the Urim and Thummim, so that they are over Aaron’s heart when he comes before יהוה. Thus Aaron shall carry judgement for the Israelites over his heart before יהוה at all times.
ויאמר שאול אל ה’ אלהי ישראל: [למה לא ענית את עבדך היום. אם יש בי או ביונתן בני העון הזה, אלהי ישראל, הבה אורים. ואם ישנו העון הזה בעמך ישראל] הבה תמים
Septuagint version:
Saul said to the Eternal the God of Israel: [Why do you not answer your servant today? If the fault is in me or in Jonathan my son, O God of Israel, give Urim, and if the fault lies within your nation Israel,] give Tamim.
(6) And Saul inquired of the Eternal, but the Eternal did not answer him, either by dreams or by Urim or by prophets.
(1) את האורים ואת התמים THE URIM AND THE THUMMIM — This was an inscription of the Proper Name of God which was placed between the folds of the breast-plate through which it illuminated its words (m'eir) and completed its words (metamem) (Yoma 73b). In the second Temple there was certainly the breast-plate for it was impossible that the High Priest should have lacked a garment, but that Divine Name was not within it. It was on account of the inscription which constituted the Urim and Thummim and which enabled it to give decisions that it was called “judgment”, as it is said, (Numbers 27:21) “And he shall enquire for him by the judgment of the Urim” (Numbers 27:21).
Even though a decree of a prophet can be retracted, a decree of the Urim VeTummim cannot be retracted. As it is stated: “By the judgment of the Urim” (Numbers 27:21). Why is it called Urim VeTummim? Urim, which is based on the word or, light, is so called because it illuminates and explains its words. Tummim, which is based on the word tam, completed, is because it fulfils its words.
Apparently, Urim designated fault or bad, (probably based on the word ארור = cursed), andTamim implied good (probably based on the word תם = perfect). Saul wanted to see who is at fault. If Urim will be the result then it’s a sign that he or his son is guilty, if Tamim will be the result, the fault must lie with someone else among the Israeli nation.
In light of the reconstructed text, it seems plausible to surmise that when Saul “asked advice from God” he employed the Urim VeTumim, as in most other cases where the term וישאל באלהים is used, and The Urim VeTumim worked by throwing lots, which were probably two stones or tablets inscribed with the words “Urim” and “Tumim”. Perhaps whichever fell out first, or in proximity to the accused, defined the result. Note, it seems that a definite answer could not always be obtained from the Urim VeTumim, as in our case where Saul complained that God did not respond the first time, so it seems likely that using the Urim VeTumim was more complicated than throwing regular lots.
The NIV Application Commentary: Esther by Karen H. Jobes

Joshua Trachtenberg, Jewish Magic and Superstition, 1939
Casting lots (Sortilege) was a common divinatory practice during the Middle Ages. Though such simple devices as tossing a coin, throwing dice, etc., were employed, the procedure even in these cases was complicated by rules specifying when the operation might be performed, and just how the lot was to be held, and how to interpret the results, as well as by the recitation of prescribed prayers or charms. A form of lot which the Jews learned from “Esclavonia” utilized a piece of wood from which the bark had been peeled on one side; the smooth side was denominated the “woman,” the rough, the “man.” It was tossed into the air twice. If the “man” fell uppermost the first time, followed by the “woman,” this was a good portent; the reverse betokened ill luck, and two of a kind was taken to be non-committal. There were also Hebrew “Books of Lots” which, like their Christian counterparts, were of Arabian origin; the Jewish versions appear to have been composed mainly in Southern Europe and in the Orient. They were probably used in the North as well, but there is no such work which can definitely be traced to Northern Europe. These works comprised sets of rules for finding answers to specified questions by means of the twelve signs of the Zodiac, the twenty-two letters of the alphabet, the names of the twelve tribes, animals, birds, cosmic phenomena, etc.
(33) Lots are cast into the lap; The judgement depends on the Eternal.