Below are some common mechanics found in various card games.
Discard - player removes a card from his hand and puts in out of play or into a graveyard/trash pile
Draw - player draws a card from a deck
Deck - a stack of cards that players draw from. Can be communal or personal.
Play - Playing a card usually refers to activating or using a card in the player's hand. The card is publicly displayed and depending on the card, may remain in play or be discarded once the card's ability has been used.
Suit - "Color" or "Family" the card belongs to. In a 52 deck, there are suits of spade, clubs, diamonds and hearts. In Magic, there are colors of white, black, red, blue and green.
Hand building - In Poker, players win by constructing a hand with the highest value, or by decieving the other players into thinking they do. Part of Dominion's essential experience is allowing players to build powerful hands that let the player use all of the cards in it sequentially.
Attacking/Defending - In the 52 deck game "War" players attack each other with cards of various numbers. The highest number wins. In Magic, players attack and defend with summoned creatures and spells.
Buying/Selling - In Dominion, players use coin cards to buy action cards that they will later shuffle into thier hand. In Magic, players use mana cards to pay for summoning creatures and casting spells. In Modern Art, players buy and sell art from fictional artists, with the hopes the ones they buy will go up in value.
Rule change cards - Magic and Dominion both feature cards that modify the existing ruleset. The modifications can be for the player using the card, or for another player. Modifications could be as simple as allowing the player to play another action, get temporary extra money, or as complex as enchanting a creature so that it is immune from damage from a certain suit or color source.
"Instants" - These are cards that you can play during another player's turn. Magic is famous for these.
"Tapping" - Taking a card that is in play and visually signalling that it is being used this turn.
Poker - Highest hand wins.
Uno - Player who gets rid of all of thier cards first wins.
Dominion - Player with the most victory points wins. Victory points are won by accumulating the most/highest value province cards. The downside of this model is that it limits the player interactions.
Magic - Player who gets to zero life first loses. The advantage of this model is that direct confrontations between players happen frequently.