AI can often be boiled down to simply choosing the best move, which is especially useful in board games like Chess, where distinct possible actions can be measured. Chess AI in particular is a case of calculating the value of the board for each player, and iterating through every possible move, then comparing the value of the board. Not every move will increase or decrease the value, but calculate a few moves ahead and the AI can pose a real challenge. Like, really Chess AI is looking for the first move in a series of moves that will win the game - and it's all done with piece valuation, with the King being exponentially higher valued than the other pieces (which are typically valued depending on the number of squares they can attack as well as if they are under threat from an opponent piece. With these fairly straightforward rules, Chess AI will defend and attack and play a decent game, you could say that Chess AI is a challenge of data management rather than clever programming.
The same basis could apply to your card game. If each player takes a turn, and there's a finite number of moves they can make, then calculate a value for each move, then if it's possible, calculate the opponent moves as well, and drill into layers of possible future moves, looking for the best scoring initial moves. Hope that makes sense.
If, just for an example, you have a card game with 2 players, and each player has 5 cards, and 1 card in the middle, the players can either put a card down of the same suit, or a card down of the same value. So if there's a 5 of hearts in the middle, and the player has a 2 of hearts, 3 of hearts, 5 of clubs, 6 of diamonds, and 3 clubs... They could play the 2 or 3 of hearts, or play the 5 of clubs, changing the suit - but that might not be a good move because there's still the 2 and 3 of hearts, changing the suit would make it more difficult to get rid of those. You AI might calculate the value of the players hand, and if a card matches the suit, adjust the value of that move, and the AI will favour moves that retain a suitable face card. The AI might suggest playing the 2 of hearts, then the 3, then the 3 of clubs, leaving just the 5 of clubs, and the 6 of diamonds. If an opponent changes the suit, then the AI would adjust - like if the 2 is played, then an opponent plays a 2 of clubs, then the AI would favour playing the 5 of clubs, then the 3 of clubs, then the 3 of hearts and on and on.
So I suggest that you consider how the game is played, what moves are valuable, how can you score a players hand to compare different possible moves. I think that the old fashioned Chess brute force method of assigning values and calculating scores would provide awesome AI, like scary stuff that will beat you, it can get very interesting once you start to meddle with this stuff.