Prophecy is all over the place in fantasy, to the point where it’s enough of a cliche that a writer has to tread carefully in using it. The Chosen One who will save everybody from the evil threat, the return of an ancient foe when certain conditions are fulfilled, etc. etc. . . . been there, done that, could make a t-shirt out of the book covers.
Weirdly, though, divination doesn’t show up nearly as much. By that I mean not the giant, earth-shaking predictions of What Is to Come, but the smaller, day-to-day attempts to get some supernatural guidance. This is a worldwide phenomenon, from ancient times to the present moment, because uncertainty is a universal thing in life, and so is the desire to allay it by one means or another. We watch weather reports because we don’t want to end up cold or wet; we read stock market predictions because we don’t want to lose our investments. And if we believe that there’s a way to get information from spiritual sources instead of statistical models, we’ll try that, too.
These days the most common version of that is probably the newspaper or internet horoscope. (How many of us read those with interest, even if we don’t believe?) Calculating a horoscope is a fairly complicated process, though, requiring knowledge of astronomy; if you’re talking about a pre-modern society, relatively few people are going to have the specialized education necessary to do that work. Astrologers have historically been advisers to the rich and powerful, who can afford to hire skilled professionals. For everyone else it was more often about seeing general omens in comets, shooting stars, solar and lunar eclipses. (Almost all of which tended to be interpreted as signs of calamity, though occasionally they heralded important births.)
Today most of us think of astrology as idle diversion at most, but it used to be very serious business. In Tudor England, calculating the horoscope of the king or queen was a crime, because you might be trying to determine when and how they were going to die. In the urban fantasy manga Tokyo Babylon, the two onmyōji (yin-yang magicians) conceal the times and places of their births from each other, as a form of supernatural security. Onmyōdō, which is the Japanese term for a practice that originated in China, made widespread use of astrology in general to calculate auspicious and inauspicious days and directions; one day might be favorable for war, while on another day court nobles would avoid any business that required them to travel south, because that direction was temporarily ill-omened. Celestial bodies are sufficiently awe-inspiring, and sufficiently associated with the gods and other powerful spiritual forces, that it made sense to assume their movements and alterations were a message to or influence on the earth below.
You’ll sometimes see tarot in fiction, usually urban fantasy, where the writer leverages it to create foreshadowing or move an investigation forward by providing insight to the protagonist. Tarot-as-divination (contrasted with tarot-as-game) is a more recent phenomenon than many people assume, but in a secondary world you can make it as old as you like. Or invent your own version: the Pathfinder roleplaying game has a surprisingly good deck called the harrow, with an interpretive system that isn’t just the tarot with a paint job slapped on top. But decks of cards as a widespread thing, whether for divination or just play, pretty much requires your society to have at least woodblock printing technology; if they’re being made entirely by hand, they’ll be quite expensive and rare.
When runes or bones show up in fiction, they’re often much more handwavy, with some old crone tossing them onto the ground and then declaring whatever the plot needs. I suspect this is largely because readers and writers alike are less familiar with those methods, so there’s less expectation that you’ll show your metaphysical math. And while there’s a relatively codified system for runic interpretation, at least as it’s performed nowadays, the more generic “bones” are far less defined. We know that in Shang Dynasty China they used turtle plastrons and ox scapulae for divination, by interpreting the cracks created when a hot rod touched the material — but the principles behind that interpretation? Those are lost to time, at least until some archaeologist digs up an ancient Scapulomancy 101 text. Much more well-known is the I Ching, which can be cast with coins or yarrow sticks (though how the latter used to be done is again unclear).
Some kinds of divination are the realm of governmental officials and other formal figures, like the haruspices of ancient Rome or the onmyōji of Japan. In the highlands of Guatemala, the Mayan tzolk’in calendar is still used by daykeepers who must undergo a lengthy initiation; I was fortunate enough to take a class once from Dennis Tedlock, who along with his wife Barbara has been initiated as a daykeeper as part of his anthropological research. But other forms of divination are very much folk magic, accessible without a long period of training or official certification. bibliomancy can be employed by any literate person with a book in their house (in Christian Europe, usually the Bible). The behavior or animals or appearance of unusual cloud formations are there for anyone to see, and over time you’ll get a handful of set interpretations, like the Japanese belief that a butterfly entering the guest room a house means a loved one is coming to visit. In colonial New England girls would toss apple peels over their shoulders, which were supposed to land in the shape of the initial of the man they were to marry. (I remember reading a novel where the protagonist complained that hers always broke apart into nothing legible, but I don’t recall which book that was.) Virtually any phenomenon, from the clumping of tea leaves to the barking of dogs, can be interpreted for information on the past, present, or future.
I don’t expect that to go away. Science fictional futures where everybody is 100% rational and never expresses superstition or religious belief are more difficult for me to believe in than faster-than-light travel. And in fantasy, you’d expect to be everwhere. But even there, divination is rarely present. As authors, we reach for prophecy when we need it to steer the plot, but we forget to think about the aunt who pulls out her copy of scripture any time she has to make a decision, the queen who scrupulously observes directional taboos, the military commander who ignores the sacred chickens. This kind of thing used to be pervasive, shaping many small decisions instead of just the big ones, and a story that remembers that will feel a lot more real.