What mattered was what the community in which the crime took place thought. If you could produce witnesses you could vouch for your good character, and from Anglo-Saxon times status counted, so a thegn's evidence - like his life - was legally worth more than a churl's. Those accused of a crime who were unwilling to pay the standard fine could also hope to clear their names by swearing oaths to God - this was popular in the early Middle Ages and called ‘compurgation‘: a person accused of a crime swore on oath that he or she was innocent and often had a number of associates swear the oath with him to 'prove' guilt or innocence. This system was understandably open to abuse, so by the ninth century the church actively backed another way to reveal God's judgment in any crime - by means of the ordeal.
An ordeal was precisely that - a trial the accused could undergo to submit to the divine and so prove they were not guilty. The term ordeal has the meaning of "judgment, verdict" in old English and in the Middle Ages many believed they were genuinely submitting to the judgment of God.
In the ordeal of boiling water, a man would plunge his hand or arm into a cauldron of boiling water, after which the hand would be bound up, sealed with the seals of the church and then left. After three days the bandages would be removed and if the man showed signs of scalding he would be pronounced guilty.
There was also ordeal by combat, also known as 'trial by battle', a way of ‘proving’ guilt or innocence that was much favoured throughout the Middle Ages. Introduced into England by the Normans, the earliest case in which trail by battle is recorded was Wulfstan v. Walter (1077), eleven years after the Conquest, possibly between a Saxon and a Norman. By the 12th century it was the way nobles would often settle disputes. The parties fought on a duelling ground and swore before they began that they had not used witchcraft to help them.
Women were usually banned from taking part in such trials but not always, a detail I exploit in my novel, A Knight’s Captive. In parts of Germany a woman might fight a man in a trial of battle if the man had one hand tied behind his back. Lepers were banned from fighting in ordeals but hired champions could sometimes be used - these were usually desperate men, since they could be killed in the ordeal of battle, or afterwards hanged or lose a hand or foot if they were judged to have lost. In medieval France the professional champion was seen in the same way as a prostitute.
Of all the ordeals, trial by battle remained in force the longest - it was not abolished in England until as late as 1819.