Playing cards were adopted from Asia in modified form by Europeans in the early 1400s. There was no one ruleset that dominated, since this was long before standardization of such things, and it was not as if a single company developed the cards.

However, the earliest common games played were forms of tarot and its relatives. Tarot is a trick-taking game (like hearts, bridge, or rook). That is, players play multiple rounds, or "tricks", using the cards in their hands, with the highest-value card winning each trick. The player with the most points after the hand has been played out wins.

A tarot deck has 78 cards. 56 of them are very similar to modern playing cards, which are derived from them. There are 10 number cards in each of the four suits (in the original Italian format: clubs, coins, cups, and swords) and four face cards. The face cards are jack (knave/squire), knight, queen, king. The 22 remaining cards are trumps that outrank the other four suits (these are the fancy ones that occultists like).

Modern playing cards simply eliminated the trumps and the knight card, leaving a deck of 52 cards.

I question the assertion that Tarot games are oldest. Do you have a reference for that? Tarot games are undoubtedly old but I dont think there's evidence that they are older than fishing games or game such as Karnoffel.

Parlett has suggested that "fishing" games such as Scopa maybe oldest. We believe cards were introduced to Europe through Italy and perhaps Spain about 1377. And then swept north. Tarot games are played in Italy but they are most prevalent in eastern Europe so there maybe some support for that theory. However fishing games are still played in Spain and Italy which also supports their early origins.

parlett also cited some north african fishing games which may be similar to what was played first. The fact that they are called "fishing" also suggests that they got their name at the very time cards were entering europe via port cities. You wouldnt call a game a fishing game if you hunted in the woods, or at least not likely.

The oldest trick taking game we know the rules to is Karnoffel (trans: hernia) which dates from about 1420. I dont think we know of Tarot before that time although it is possible. Parlett believes that card games would have evolved one stage at a time, with the idea being that you would go from a fishing game, to a trick taking game w/o trump, to then introducing trump. SUggesting that Karnoffel would come after fishing games.

If you but into that theory of progression then presumably a plain trick game should come before a game with trumps. Although that is open to interpretation. For example if everyone plays a card in turn that is a trick, but fishing games work the same way, just that the players capture cards already on the table. It is arguable what is simpler: a plain trick game or a fishing game as they have a lot in common. Presumably tarot games with trump would be later.

Karnoffel is odd, because it has partial trumps (they dont beat every card of the other suit but only cards up to a certain rank) but quite sophisticated. You can find similar games buried in odd places in Europe such as the Valtelline in Swiz or in Iceland because those areas were cut off from european culture and so primitive games still exist there. Karnoffel apparently drove the authorities crazy because it had high cards such as the pope being beaten by low cards; preachers even railed against it.

Icelandic games such as Alkort and Triekort are also played with partial trumps like Karnoffel and so may represent some primitive trick takers that have existed in Iceland from a time long ago.

Source: David Parlett The History of Card Games (copyright approx 1980)