The word divine comes from divination, which in a broad sense means getting information from a divine being. The divine being can be a god, goddess, angel, any kind of spirit, or some other supernatural entity. While still holding this meaning, divination today normally refers to attempts to get information by reading hidden meanings in images, patterns, or the natural world (such as finding meaning in cards or the position of planets in astrology), or via attempted contact with supernatural beings (angels or other disembodied beings), or via supernatural means (such as the use of psychic abilities).
Words ending in mancy almost always refer to a form of divination. Mancy comes from the Greek manteia, which means divination. Divination is very central to occult practices and is forbidden and strongly denounced by God in His word. Deuteronomy 18:10-12 lists all the practices of the occult, including divination (which may be translated as "fortunetelling" in some translations). Divination is also condemned in 2 Kings 17:17, 21:6; 2 Chronicles 33:6; Ezekiel 23:13; Acts 16:16; and others.
Some of the forms of divination used in the Old Testament include scattering arrows on the ground (probably to read the patterns) and looking at the liver of dead animals. Ezekiel 21:21 refers to these: "For the king of Babylon stands at the parting of the way, at the head of the two ways, to use divination; he shakes the arrows, he consults the household idols, he looks at the liver."
Arithmancy is divination using numbers, especially when letters of the alphabet are converted into numbers, such as in numerology. Arithmancy is in the Harry Potter books as a subject taken at Hogwarts by Harry and his classmates.
Bibliomancy is seeking to find a private message in a book, especially the Bible, by opening it at random. This does not mean that you cannot open the Bible and find a passage that is meaningful to you, but rather, it is a belief that there is a message or answer especially for you (and no one else) which is found only by opening the book at random.
Cartomancy is reading cards, such as Tarot card readings.
Chiromancy is divination by reading the palm.
Geomancy is reading meaning in the features of landscapes or structures. Feng Shui is a form of geomancy.
Necromancy is divination via contact with the dead. Merely contacting the dead is spiritism, such as is allegedly done on some television shows featuring "haunted" houses, "ghosts," etc.. A medium is someone who claims communication with the dead which may be done by the medium receiving messages from the supposed dead, or by letting a disembodied "guide" speak through him or her with messages from the dead (this guide is called a "control"), or by channeling the voice of the dead person. If one is attempting to contact the dead for messages or advice about the future, that is necromancy. Therefore, mediumship or consulting a medium is engaging in divination as well as in spiritism.
There are, of course, many words for divination methods that do not end in mancy. Some examples are:
Astrology - Reading meaning in the positions and patterns in the planets.
Scrying - Reading messages in opaque surfaces, such as a crystal (the opaque surface is actually used as a point of concentration for the reader). However, this is also known as hydromancy.
Augury - Reading messages in the patterns or formation of birds in flight. "The augur was a priest and official in the classical world, especially ancient Rome and Etruria. His main role was to interpret the will of the gods by studying the flight of birds: whether they are flying in groups or alone, what noises they make as they fly, the direction of flight, and what kind of birds they are. This was known as 'taking the auspices.'" From http://en.wikipedia.org/wiki/Augury
Belief in omens means that certain events indicate a forthcoming happening, good or bad. Examples are: the appearance of a comet means a disaster is on the horizon; if you drop a spoon, you will have a visitor; or a black cat crossing your path forebodes bad luck. Many of these beliefs are a part of folk tales and garden-variety superstitions (such as 7 years of bad luck for a broken mirror).
Almost anything can be used for divination: Using a pendulum to get advice, even just a "yes" or "no" answer; dowsing, whether using branches, wire, or other object, to find water, buried treasure, oil, etc.; tying a pencil at the end of a string and holding it while asking a question to see which way it sways; and applied kinesiology (muscle testing) is a form of divination mixed in with New Age pseudo-science.
An object (such as pencil or branch) without a link to an intelligent source or a non-thinking organism (such as a muscle or liver) cannot provide supernatural information or guidance. When one is going beyond the normal five senses to get information or advice or answers, then it is very likely to be divination.
Divination replaces seeking the counsel of God and puts one at risk for contact with fallen angels, who are only too happy to disguise themselves as the dead, as good angels, as aliens, as "higher beings" on another plane, or whatever, in order to deceive. (2 Corinthians 11:14).
Terms for methods of divination (note that most of these end in mancy,
though not all)
This link gives more examples:
At the link below, scroll down and click on "terms derived from -mancy" and
quite a long list will appear.