The standard ranking of poker hands is below, listed from highest to lowest. All standard poker hands are made up of exactly five cards (no more, no less).
The top five cards in a single suit: 10, J, Q, K, A all of the same suit. Really, a Royal Flush is just the best possible straight flush. There can be no ties in a hand with royal flush, as there is only one card of a number and same suit. for example there can only be one "10 of hearts"
A straight flush is five cards in rank sequence, all in the same suit. Straight flushes are named for their highest card (e.g. "A 7-high straight flush"). As in a straight, the Ace may be considered high (10-J-Q-K-A, making a Royal Flush) or low (A-2-3-4-5, making the lowest possible straight flush). Ties between straight flushes are broken the same way that ties between straights are: by the highest card in them (a Jack-high straight flush beats a 9-high straight flush).
Four Of A Kind
Also called quads. Holding all four cards of a given rank is four-of-a-kind. Quads are named for the card in question (e.g. "Quad 8's", or "Four 8's"). Ties between fours-of-a-kind are broken by the rank of the quads (four 8's beat four 6's). Ties between quads of equal rank are broken by the single-card kicker that forms the fifth card of the hands (four 8's with a King kicker beats four 8's with a Jack kicker).
Also called a full boat or a boat. Holding three cards of one rank and two of another rank (or, in other words, having a three-of-a-kind of one card and a pair of another). Full houses are described as "CARD-A's full of CARD-B's", as in "8's full of 3's", or "Jacks full of Aces", where the first card mentioned is the rank of the card there are three of and the second is the rank of the pair. For example, Jacks full of Aces means holding three jacks and two aces. Ties between full houses are broken by the rank of the three-of-a-kind card (8's full of 3's beat 7's full of Aces). If there is still a tie, it is broken by the rank of the pair (8's full of 3's beat 8's full of 2's).
Holding five cards all of the same suit. Flushes are named for the highest card in them (e.g. a flush that contained a King but not an Ace would be called a "King-high flush"). Ties between flushes are broken by ordering the cards from highest to lowest and breaking the tie as you would a High Card hand: the flush with the highest card in it wins; if that is still tied, the flush with the highest "second-high card" wins; if that is still tied, the flush with the highest "third-high card" wins; etc. If all five cards of the suits are the same for both hands, the hand remains tied.
Holding five cards in sequential rank, regardless of their suit. For purposes of this sequence, an Ace may be counted as high (coming after a King) or low (coming before a 2). Suits are not counted in straights. Straights are named by their highest card: a straight of 4-5-6-7-8 would be called an "eight-high straight", and "10-J-Q-K-A" is called an "Ace-high straight". If an Ace is being used as low (for A-2-3-4-5), it is called a "five-high straight" (since the Ace is low, it is not the high card in the straight). Ties between straights are broken by the highest card in them: an eight-high straight beats a six-high straight. So-called "wrap around" straights (using an Ace as both high and low in a single straight, such as Q-K-A-2-3) do not count as straights in poker, unless a particular home game has decided to count them as such.
Three Of A Kind
Also called trips or a set. Holding three cards of the same rank. Ties between threes-of-a-kind are broken by the rank of the card in question: three 8's beats three 5's. If both hands have three of the same rank (for example, both hands have three 8's), ties are broken by the highest two-card kicker: three 8's with an Ace-Queen kicker beats three 8's with an Ace-Nine kicker.
Holding two separate pairs of two different ranks. Two-pairs are named by naming the two pairs in them, highest pair first ("Jacks and Fours", not "Fours and Jacks"). Since it is often sufficient to merely name the highest of the two pairs (see the tie breaking bit, next), two pairs are also often named only by their highest pair, along with the suffix "up", such as "Aces up", or "Jacks up". Ties between two-pairs are broken by the rank of the higher of the two pair: 9's and 2's beats 7's and 6's. If both hands have the same higher pair, ties are broken by the rank of the lower pair. If both hands have the same higher and lower pair, ties are broken by the rank of the one-card kicker: 9's and 2's with a Jack kicker beats 9's and 2's with a 5 kicker.
Holding a pair of cards of the same rank. Pairs are named by naming the rank (e.g. "A pair of Queens"). Ties between pairs are broken by the rank of the pair: a pair of 10's beats a pair of 7's. If both hands have the same pair, ties are broken by the ranks of the three-card kicker: A pair of 10's with an Ace-Queen-Four kicker beats a pair of 9's with an Ace-Ten-Five kicker.
Holding a hand that has no pair, no sequence of five in a row, and no set of five cards in the same suit. Hands with a high card are named by their highest card (e.g. "Ace-high" for a hand that contains an Ace but nothing else, or "9-high" for a hand that contains a 9 but no higher card). Ties are broken by the highest card in the hand; if both hands contain the same highest card, ties are broken by the second highest card in the hands. If the tie remains unbroken, it is broken using the third-highest card, and so on, down to the fifth-highest card in the hand. For example, "King-Jack high" beats "King-Ten high".