This is a work-in-progress!

POKER BASICS

What is poker?

Poker is a card game played for money.
It doesn't work without the money, and how you bet is as important as anything you do with the cards.
There are very many variants, but in all cases you somehow end up with a hand consisting of 5 cards.
These hands are ranked according to how the cards match up with one another, and the player with the best ranking hand wins.

There is also a variety of betting structures, from fixed size bets to completely unrestricted betting.
The size of the basic bets varies too: there are games where a single bet will cost you $5000, and somewhere there is a game where the bet is 1p.
Most of us play in games with bets somewhere in-between!

That's OK as a definition, but it doesn't really tell me how it works
A bunch of guys sit round a table: there can be as many as 10, and the game has different dynamics when you get down to 4 or less but can be played with just 2.
Usually you buy some chips from a banker when you arrive, and use those to bet instead of real money.
Either the players take it in turns to deal, or (eg in a casino) there may be one dealer and a marker (the 'button') to show where the deal starts.
In each hand, the dealer shuffles, somebody cuts, the 'ante's and/or 'blind' bets go in, and the first cards are dealt out.
Everybody has a look at what they've got and the betting commences...
In turn, from "1st to speak", who is (usually) on the dealer's left (or the big blind's left in the first round):
players with bad cards will save their money by 'folding' and passing their cards to the 'muck', taking no more part in that hand;
players with good cards will join in the betting;
players with very good cards will increase the bet, and this may cause some more to fold.
When it's gone around and everybody who wants to stay in has put the same amount of money into the 'pot',
the next cards are dealt, then there's some more betting, and so on according to the particular variation being played, until finally...
either one player bets more than anybody else is prepared to match and he takes the pot without having to show his cards at all,
or the players still active at the end compare their hands in the 'showdown' and the best ranking hand takes the money.
Then the deal moves on and it all starts again.

Hand rankings

The rankings are ordered according to the true probabilities of the cards matching up as if 5 cards were drawn at random,
however many cards were involved in the particular variant being played and whatever the mechanics of getting them.
The only deviation from this is in some low-hand-wins games where straights and flushes may be disregarded altogether.

The HANDS - Highest to Lowest

NB. Aces normally count as the highest card, but can be used as a 1 in straights and in some low-hand-wins games.
FIVE OF A KIND 5 cards of one rank (only possible when playing with wild cards) AAAAA ... 22222
STRAIGHT FLUSH 5 cards of one suit in sequence AKQJT ... 5432A
FOUR OF A KIND (quads,box) 4 cards of one rank (and 1 other card) AAAAx ... 2222x
FULL HOUSE (boat) 3 cards of one rank, 2 of another rank AAAKK ... 22233
FLUSH 5 cards of one suit, not in sequence
Suits are not ranked, eg AJ854 in hearts ranks equally with AJ854 in clubs
AKQJ9 ... 75432
STRAIGHT 5 cards in sequence, different suits AKQJT ... 5432A
THREE OF A KIND (trips, set) 3 cards of one rank (and 2 other cards) AAAxy ... 222xy
TWO PAIRS A pair of each of 2 ranks (& 1 other card) AAKKx ... 3322x
PAIR 2 cards of one rank (and 3 other cards) AAxyz ... 22xyz
HIGH CARD All different ranks, more than one suit AKQJ9 ... 75432

Betting Terminology

ANTE From the Latin for "before": an amount paid by each player before the deal in order to be in the hand, and to start the pot.
Sometimes replaced by a single 'sweetener' from the dealer. Antes are not used in all games.
BLIND Instead of (or as well as) antes there may be 1 or 2 "blind" bets by the players to the dealer's left. The blinds get the pot started and force the poor "early position" players to play at least a bit.
Blinds are normally "live", ie they may raise even if this means raising their own bet, which is not otherwise allowed (see RAISE).
The 2nd (or only) blind usually equals the minimum bet; if there are 2 blinds then the first ("small") blind is usually half the second ("big") blind.
CHECK A bet of nothing, keeping a player in the hand without committing real money. You cannot check after someone has bet in any round (including blind bets), as everybody who stays to the end of the hand must put in the same amount of money. You may not (usually) check in the first round in stud games.
OPEN The first bet of a betting round. In stud games, it's usual that the player who is 1st to speak must open.
CALL To match the previous bet(s). To stay in a hand you must call all bets, so that all players who remain active contribute the same money.
RAISE To match the previous bet(s) and add more. Players wishing to stay in the hand must call the raise. You cannot raise your own bet (unlike that ridiculous game Brag). Usually raises must be at least as big as the preceding bet. There is usually a limit of 3 raises in any betting round, except perhaps in the last round, or whenever there are only two players still active.
FOLD or PASS To give up. You lose any money you had bet so far.
The POT All that lovely money in the middle.
SIDE POT If anyone runs out of money, the others start a separate pot. Only they can win this side pot. Anyone can win the main pot.
SPLIT POT Some games split the pot between the highest and lowest hands. Also, if 2 players' hands rank exactly the same, they split the pot.
1ST TO SPEAK In stud games, the player with the best upcards (or lowest, in the 1st betting round, in most places: check!). In draw and flop games, the player to the dealer's left (or to the left of the blinds in the 1st round), or sometimes the player who opened the previous round or was last to raise in the previous round.

BETTING LIMITS

Poker is often played with fixed size bets, usually doubled for the last betting rounds (last round in draw, last 2 rounds in 7stud, ie approx half the betting rounds).
There is usually a maximum number of raises per round (often 3) except perhaps in the last round or any time a hand goes 1-on-1.
Any game (most games in the UK) can be played POT LIMIT, ie you can bet or raise any amount up to the size of the pot (if raising, the amount allowed is calculated after adding in enough for your call).
Some games are played NO LIMIT - bet what you like! - but usually any raise must be for at least the size of the previous bet.
There are other structures as well, but these are the most common.

POPULAR VERSIONS

Currently popular versions are Hold'Em, 7 card Stud, and Omaha-8s-or-better

Stud games: you get some cards and use 5 to make the best hand you can.
Draw games: you get the opportunity to exchange some cards for new ones.
Flop games: some of the cards are common to all of the players.
There are many hybrid versions, and many versions with "wild" cards.

Any version may played with lowest hand winning (when straights and flushes are often disregarded).
Many games are also played hi-lo split, nowadays usually "cards speak" but sometimes with a declare (high, low, or both).

NB. It's unlikely that everybody everywhere will agree on the exact details given below, except for the most common games

HOLD 'EM Blinds
Deal 2 'pocket' or 'hole' cards to each player, Betting round
Deal 3 common up-cards (the 'flop'), Betting round
Deal 1 common up-card (the 'turn'), Betting round
Deal 1 common up-card (the 'river'), Betting round
Showdown.
The best combination of 5 cards out of the player's 2 and the 5 common cards (the 'board') is the player's hand.
IRISH Like Hold'Em but with 4 hole cards, 2 of which are discarded after the flop.
PINEAPPLE Like Hold'Em but with 3 hole cards, 1 of which is discarded before the flop; in CRAZY PINEAPPLE it's discarded after the flop.
OMAHA Like Hold'Em but you have 4 hole cards of which you MUST use EXACTLY 2.
There are 6 ways to choose 2 cards from your 4 hole cards so the average winning hand is higher than in hold'em.
If there are 4 spades on the board and you have 1, you don't have a flush because of the "use 2 cards" rule.
OMAHA 8s OR BETTER Omaha with a hi-lo split, but reverting to hi-only if there is no 8high or lower for the lo hand - and there must be 3 cards 8 or lower on the board for that to be possible
DENTON A Hold'Em/Omaha hybrid: you have 3 hole cards of which you may use 1 or 2 - ie not all, and not none.
7 CARD STUD Ante
Deal 2 'hole' cards face down and 1 'door' card face up to each player, Betting round
Deal 1 card face up to each active player, Betting round
Deal 1 card face up to each active player, Betting round
Deal 1 card face up to each active player, Betting round
Deal 1 card face down to each active player, Betting round
Showdown.
Best 5 of 7 is player's hand.
7stud is sometimes played hi-lo split
CHICAGO 7stud with the rank of your low hole card wild.
"That way madness lies" as somebody like Shakespeare once wrote.
RAZZ 7 card stud played low-hand-wins.
Straights and flushes are disregarded, Ace is low: there's also a A-6 and a 2-7 version of 7stud Lo.
4 out of 5 hands are very boring: the other gives you a heart attack.
5 CARD STUD Ante
Deal 1 'hole' card face down and 1 card face up to each player, Betting round
Deal 1 card face up, Betting round
Deal 1 card face up, Betting round
Deal 1 card face up, Betting round
Showdown.
Rarely played nowadays
MEXICAN STUD As 5 Card Stud but all the cards are dealt down, and the player chooses which to turn up at each round.
DRAW Ante
Deal 5 cards to each player, Betting round
Each active player, starting at the dealer's left, may exchange some cards for newones, Betting round
Showdown.
Also often played with various wild cards, eg all deuces, or just the black deuces, or one-eyed jacks, or a joker which can be an ace or any card in a straight or flush, or.....
JACKPOTS As Draw, but you must hold a pair of Jacks or better to open.
Opener's discards are kept for checking he did qualify to open, if necessary.
In some places, if nobody can open then the next hand is a Queenpot, and if nobody can open that then the next is a Kingpot...
LOWBALL As Draw, but lowest hand wins.
There are versions where straights and flushes are disregarded, and versions where they aren't
Triple Draw Lowball is currently popular. I think it's crazy.