The commentaries I consulted did not have an authoritative answer nor a convincing suggestion. I suspect that what was being referred to is "scrying":
One looks intently at any of a variety of reflective surfaces such as a metal cup, a crystal ball, a chicken's liver, obsidian stone (such as arrow heads), a pond, etc. and interprets the obscure reflections therein.
Since Joseph had earned a reputation of accurately interpreting dreams he may have been esteemed as a diviner and used his reputation to lend credence to his fabricated story to his brothers:
Jamieson-Fausset-Brown Bible Commentary 5. Is not this it in which my
lord drinketh—not only kept for the governor's personal use, but
whereby he divines. Divination by cups, to ascertain the course of
futurity, was one of the prevalent superstitions of ancient Egypt, as
it is of Eastern countries still. It is not likely that Joseph, a
pious believer in the true God, would have addicted himself to this
superstitious practice. But he might have availed himself of that
popular notion to carry out the successful execution of his stratagem
for the last decisive trial of his brethren.
Micah 3 seems to suggest that some prophets in Israel were "diviners":
NIV Micah 3: 5This is what the Lord says: “As for the prophets who
lead my people astray, they proclaim ‘peace’ if they have something to
eat, but prepare to wage war against anyone who refuses to feed them.
6Therefore night will come over you, without visions, and darkness,
without divination. The sun will set for the prophets, and the day
will go dark for them. 7The seers will be ashamed and the diviners
disgraced. They will all cover their faces because there is no answer
from God.” 8But as for me, I am filled with power, with the Spirit of
the Lord, and with justice and might, to declare to Jacob his
transgression, to Israel his sin.
Micah does not condemn the practice explicitly but he does attribute his own success to power and virtue from God.