One simple method was cruentation, from Latin ius cruentationis, "law of bleeding," used in Germanic law. The belief behind cruentation was that the corpse of a murder victim would indicate the presence of its murderer by moving or spouting blood. It was used into the 18th century, even though after the Lutheran Reformation the application of a religious test in law was rejected in Denmark and Norway.
Another approach to Trial by Ordeal was the idea that God would not allow an innocent person to suffer. The accused would plunge his or her hands into boiling water, or carry red hot iron. Ordeal by fire was also tried, with the person walking at least three paces or walking across nine feet of coals. Of course this would produce burns, but they would be bandaged and re-examined in three days' time. A priest would then judge whether God had chosen to heal the innocent person's burns or let the guilty person's worsen and fester.
In Constantinople, before Michael VIII Paleologos (1224 - 1282) became emperor, he was accused of treason by Emperor John III Vatatzes and was ordered to go through trial by fire. He said he would hold the red-hot iron if the metropolitan bishop Phokas would take the hot iron from the altar with his own hands and place it in Michael's. This the bishop refused to do; the idea that innocents would not also be harmed by red-hot iron helped to discredit the practice. In fact, when Michael became emperor, he abolished the practice.
Pope Innocent III at the Lateran Council of 1215 forbade priests to take part in such things, and promoted compurgation instead.
The Byzantine Empire got the idea of trial by ordeal from the West, as the Crusades brought Western Europe ideas to Constantinople. One example they would have witnessed was the French mystic Peter Bartholomew, who submitted himself to ordeal by fire to prove his sincerity about a claim considered outlandish by others. What was he trying to prove, and how did it turn out? I'll tell you tomorrow.
