"American Rules" are described here, see Rule Variations below for changes in "British Rules"
Euchre is a 4-player trick taking card game with two teams. The object is for your team to reach a predetermined amount of points before the other team does.
The Deck consists of the 9, 10, Jack, Queen, King and Ace of each suit, making 24 cards total.
Each player is dealt a hand of 5 cards. The hand is sorted by suit, then rank Clubs, Diamonds, Spades, Hearts. An "Up Card" is laid down in the center, for use in Making Trump. The remaining cards are hidden and not used in playing out the hand. Making Trump At the start of each new hand, the Trump suit must be selected. Once trump is selected, play begins. The team which makes trump are called the "Makers" and the opposing team are called the "Defenders".
The Up Card
In the first round of Making Trump, each player in turn chooses whether or not to accept the suit of the Up Card as the trump suit. If the Up Card is accepted, the Dealer picks up the card and discards a card from their hand.
Selecting a Suit
If nobody accepts the Up Card, then the Up Card is discarded and each player is given the opportunity to select one of the other 3 suits to be trump. If all 4 players pass a 2nd time, the hand is thrown in and a new hand is dealt.
The player who makes trump may also choose to Go Alone. When Going Alone, the player's partner sits out the hand. If all 5 tricks are won, 2 bonus points are awarded to the team, otherwise scoring is normal. Scoring Makers earn 1 point for winning 3 or 4 cards, or 2 points for winning all 5. If a Maker Goes Alone and wins all 5, 4 points are awarded. The Defenders earn 2 points for winning at least 3 of the tricks. The first team to earn 10 points wins the game.
How to win a trick
Once the the 1st player leads a card, every other player must follow suit if able. The player with the highest value card in that suit wins the trick. If any Trump cards are played, then the highest value Trump card wins the trick regardless of the lead suit.
This is a tricky part of Euchre.
The highest Trump is the Jack of the selected Trump suit. The 2nd highest Trump is the Jack of the same color as the selected Trump suit, and this card is considered to be part of the Trump suit. Other suits rank normally, with Aces high.
So if Clubs are Trump, the Jack of Clubs is highest, the Jack of Spades is next, then the Ace of Clubs, the King of Clubs, the Queen of Clubs, the 10 of Clubs and the 9 of Clubs. Ties for 1st The game does not allow ties for first place. In the case of a tie for first, the game will continue until there is a clear winner. This is true of both games ending at a point value and timed games.
This variation makes several changes to the game rules A Joker is added to the deck for 25 cards total. The Joker is the highest Trump. If the Joker is dealt as the Up Card, the dealer selects any of the four suits to be Trump, picks up the Joker and discards a card.
The Dealer's Partner may not accept the up card without also going alone.
The game ends at 11 points instead of 10.
In a Long Game, the game ends at 15 points instead of 10 or 11.
In a timed game, the game ends after a set time period instead of a particular point value. The player picks the time before playing. When that time elapses, you will finish the current hand, then the game will be finished.
Cut Throat Euchre
This is a variation for 3 players in which each player plays for themselves. A smaller deck is used, with the 9s removed. The player Making Trump plays alone in that hand against their two opponents. The Maker earns 1 point for winning 3 or 4 cards, and 3 points for winning all 5. If the Maker fails to earn 3 cards, each opponent scores 2 points.