My friend and I have spent a few hours researching on our own and have come up... not necessarily empty-handed, but grasping straws with new age woo where authors impose their ignorance on the reader as if it's fact. We are curious about the overall history of Tarot cards and their function/purpose in history. I apologize for the rather broad question. We are also open to book recommendations! Thank you!
As far as book recommendations go, you might get something out of A Wicked Pack of Cards: An Occult History of the Tarot, by Michael Dummett, Ronald Decker and Thierry Depaulis.
That link goes to a review that summarizes the broad sweep of the book.
Unlike /u/Freiheit_Fahrenheit/ I'm not sure Crowley was as instrumental in spreading the use of the cards as other figures who were around at about the same time or immediately prior - he was basically borrowing and repurposing stuff from the Golden Dawn, who were passing along traditions (or "traditions") from Eliphas Levi (a Frenchman with a Hebrew pseudonym) and the Theosophical Society (founded by Helena Blavatsky, a Russian living in New York).
Levi and the Golden Dawn were responsible for hammering down correspondences between tarot cards and the sefirot and paths of the tree of life in kabbalah (another esoteric system that can be traced in its current form to around the 1300s, but which claims a much more ancient history).
In 1901, another Russian, P.D. Ouspensky, published The Symbolism of the Tarot, which had a great deal of currency in certain circles. (By comparison, at about the same time, Crowley was still 37 years from starting work on his Thoth deck). Ouspensky was a disciple of the Other Big (Russian) Name in turn-of-the-century occultism, George Gurdjieff.
I don't know of any historical work published about card divination prior to to the invention of tarocchi in the Italian Renaissance, but it seems likely to me that the trumps game intersected with some other set of practices using cards or counters to tell a story (some elements of which were yet to happen).
There are some theories that this is how the Yijing (I Ching) came to be in its present form in China - as a kind of parallel to a game called liubo.
Games and rules and finite sets of randomly arranged things are pretty integral to divination.
[edit: accidentally a word]
Tarocchi or Tarock or Durak is a card game popular in Southern Europe which does use the 21 trump cards which look so exotic to the anglophone world. New Age Tarot is indebted to LaVey who was indebted to a 19th century manual to the Rider-Waite deck which, in turn, was indebted to a 18th century book on Magic called «Le Monde Primitif». Sticking to the etymology of "Gypsy" as "Egyptian" it explained divination with some wild presumptions about the Old Egyptian religion. This is where the whole talk of the "Thot" or the "Arcana" is originally from.
Giacomo Casanova describes divination done with the deck common in the Anglophone world done in Russia and in «das Deutsche Gaunertum» you get another form explained based on the common northern deck. But the current pop divination is based entirely on LaVey.
If you mean: "Where did tarot cards come from?"
It's simple: they were invented for playing card games. They're just a variation on regular playing cards. But people often used randomizing devices as a way of "divining" the future. For example, an alternative to drawing cards was opening random pages of a book like the Bible or the Aeneid. Whatever it said on the page had a meaning for your future.
Christophe Poncet makes a very convincing argument they are neoplatonic allegory. Here's a sample of his work:
http://www.livinghistory.co.uk/homepages/hermes/Poncet_Lorenzo_2008.pdf