as far as the history of the tarot goes, theres no connection to spirit calling, at least not directly. theres several versions of how they came to be, but the most common one is that they were designed to be an instruction in magic. some people say egyptian in origin, others put it in the kabala, but the intent was that of instruction in a mystic practice. as luna said, none of us were there at the time, so its mostly speculation as the tarot predates most written history.
it spread so far and wide that many cultures have taken it as their own invention as well. the "gypsy" or traveler communities claim it either originated with, or moved with them from its origins.
but the tarot is based around 5 "suits" four of which found their way into modern playing cards in a slightly changed way. they comprise the minor arcana
entacles (aka spades) wands or staves (aka clubs) cups (aka hearts) and swords (aka diamonds). its important to note that some variations have diamonds being switched with spades. the pentacle is an old symbol of the element of earth. wands are fire, cups water and swords air. the 5th element is not leeloo dallas, as most movie fans think . its called various thing. ether, spirit, akasha, et alia. it's suit is the major arcana.
starting with the fool (in most decks) which represents the aspiring mystic untrained, as well as many other things and going up to.... well the last card varies from deck to deck but most of them its called the world or the universe, which represents the finality of mystic training which is supposed to be a connection with the higher energy (god, nirvana, whatever ya wanna call it)
now, it seems that every reader of tarot has a different interpretation of how/why they work, so im not going there, but as far as its use in communing with/summoning or otherwise interacting with spirits thats a much more modern contrivance. the spiritist movement was where that part of things kicked in as a broader idea, but the spiritists tended to co-opt everything. so that part came into being in the 1800s really ( not saying that some group or individuals didnt do it b4 then, just that thats where the idea came in for the mainstream)
ima do a separate post for ouija, tho itll be much shorter