General Rules

The following general rules apply to evaluating poker hands, whatever set of hand values are used.

Individual cards are ranked A (high), K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, 2, A (low, but only when part of an A-2-3-4-5 straight or straight flush).
Individual card ranks are often used to evaluate hands that contain no pairs or other special combinations, or to rank the kickers of otherwise equal hands. The ace is ranked low in ace-to-five and ace-to-six lowball games.
Suits have no value.
The suits of the cards are mainly used in determining whether a hand fits a certain category (specifically the flush and straight flush hands). In most variants, if two players have hands that are identical except for suit, then they are tied and split the pot. Sometimes a ranking called high card by suit is used for randomly selecting a player to deal.
A hand always consists of five cards.
In games where more than five cards are available to each player, hands are ranked by choosing some five-card subset according to the rules of the game, and comparing that five-card hand against the five-card hands of the other players. Whatever cards remain after choosing the five to be played are of no consequence in determining the winner. (For example, when comparing identical full houses, there are no "kickers".)
Hands are ranked first by category, then by individual card ranks.
That is, even the minimum qualifying hand in a certain category defeats all hands in all lower categories. The smallest Two pair hand, for example, defeats all hands with just One pair or No pair. Only between two hands in the same category are card ranks used to break ties. The highest single card in each flush or straight is used to break ties (the ace-through-five straight is the lowest straight, the ace being a low card in this context). Within two Two pair hands, the higher pairs are first compared. If they tie, then the secondary pairs are compared, and then finally the kicker.
For ease of explanation, hands are shown here neatly arranged, but a poker hand has the same value no matter what order the cards are received in.