If you want to get into a TCG, I strongly recommend Shadowfist as the best multiplayer game. Cost of entry is low. There is lots of strategy. Game play is fast and furious. No one is eliminated from the game, and players always have a chance to do something. They don't waste a lot of time just waiting for their turn. The player base is very friendly.

For poker, the exact rules for number of cards, how they're dealt, betting rules and the like vary from game to game but the method of determing who wins a hand (assuming at least two go to a showdown) is fairly constant: each player makes the best 5-card hand from the cards available to them and the high hand wins. The order of hands from highest to lowest:

Five of a kind (possible only if wild cards are in play)
Straight flush (cards all same suit and in order – the best of these is AKQJT of same suit and called a Royal Flush)
Four of a kind
Full House (Thee of a kind + a pair)
Flush (all of same suit but not in sequence)
Straight (all five in sequence, but 2 or more suits)
Three of a kind
Two pair
One pair
High card

If the primary part of the hands are equal, the other cards (kickers) are used to determine who wins. If all equal, hands tie. (Example, X has TT853 and Y TT863 – both have a pair of tens with 8 primary kicker, but the Y wins because his secondary 6 kicker beats X's secondary 5 kicker.)