Rules of chess:
Pieces:
There are six different types of piece:

Pawn

Knight

Bishop

Rook

Queen

King
Each player gets 8 pawns, 2 knights, 2 bishops, 2 rooks, 1 queen, and 1 king (16 pieces total). One player's pieces are light-colored (called 'White'), while the other player's pieces are dark-colored (called 'Black').
The pieces can be assigned a rough value according to their relative worth:
Pawn - 1 point
Knight - 3 points
Bishop - 3 points
Rook - 5 points
Queen - 9 points
King - Priceless
These points aren't an official part of the game and don't really make any difference. They are just a simple tool to give you a rough idea of how valuable a piece is to you or to your opponent.
The Board:
The board is as constructed and numbered as such:
The board is 8 squares wide and 8 squares tall, for a total of 64 squares. The squares alternate between light and dark (White and Black). Note that the bottom-left square (where the numbering begins) is dark. This is also the side where White will place his pieces.
The players set up their pieces on the board like so:
Note the position of the kings and queens. A queen always starts on her own color (White on a light square, Black on a dark square).
Turns:
Players alternate turns, each moving a single piece. A player has no choice and must make a move on his turn. The White player always makes the first move of the game.
Capturing:
A player may capture (remove from the game) an opponent's piece by moving one of his own pieces onto the same space that the opponent's piece occupies. The only exception is the pawn, which has a special way of capturing. You cannot capture your own pieces.
Check and checkmate:
If you move a piece so that it threatens the opponent's king (that is, could potentially capture the king on the next turn), it is called 'check.' If you move a piece so that the opponent's king is threatened and there is nothing the opponent can do to prevent you from capturing it your next turn, it is called 'checkmate.'
Movement:
Each type of piece moves in a different manner. No two pieces may ever occupy the same square. You may not move a piece if it would place your own king in check.
Pawns:
Pawns are probably the most complex of the pieces, as far as rules and exceptions to rules go. Generally, a pawn may only move 1 space directly forward (toward the opponent, away from yourself). However, the very first time any given pawn moves it has the option of moving two spaces forward instead of just one. The pawn may not 'jump' over another piece when it does this.
First move:
The first time a pawn moves, it can move either one space or two spaces forward
After the first move:
After the first move, it may only move one space forward
The pawn has a special way of capturing. The pawn is unable to capture by moving forward, as you might expect. Rather, the pawn may only capture one space diagonally in front of it:
Before:
The pawn may capture the two pawns that are one space in front of it diagonally, but not the pawn directly in front of it.
The only time a pawn may move diagonally in this manner is when it is capturing.
After:
The opponent's piece is removed from the game.
There is an exception to this way of capturing called
en-passant (in passing). If an opponent's piece moves two spaces forward, so that it is right next to your own pawn, you may, on the very next turn only, capture that pawn by moving diagonally behind it. Like so:
Set up:
Opponent moves:
You may capture:
Remember, you can only do this on the immediately following turn. This is the only time a piece may be captured by moving behind it.
Finally, if a pawn moves onto a square in the very last row, you must replace it with a Knight, Bishop, Rook, or Queen. For example:
Before:
After:
Knight:
The knight is the only piece that can 'jump' over other pieces. It has a decidedly odd way of moving. It can move either two spaces left/right and one space up/down, or it can move two spaces up/down and one space left/right. It's easiest to see this pattern visually:
Bishop:
The bishop may only move diagonally, but may move any number of spaces. It cannot jump over other pieces.
Note that, because of the way it moves, it will never be on a square of a different color than the one it started on.
Rook:
The rook may move any number of spaces vertically or horizontally. It cannot jump other pieces (the only exception to this is when the king castles, which will be described later).
Queen:
The queen is like a bishop and a rook put together. It can move any number of spaces either diagonally or vertically/horizontally. It cannot jump over pieces.
King:
The king can only move one space, but it can move in any direction.
The only time a king can move more than one space is when castling. Castling involves both the king and one rook. It's the only time two pieces may move at once.
There are a number of conditions that must be met before a player may castle:
1) The king must not be in check.
2) The rook must not be threatened.
3) None of the spaces between the king and the rook can be occupied.
4) None of those spaces can be threatened, either.
5) Neither the king nor the rook have moved yet this game.
When castling, the king moves two spaces toward the rook, and the rook jumps to the opposite side of the king.
King-side castle before:
after:
Queen-side castle before:
after:
Note that the king always moves two spaces, but the rook will move either two or three depending on which side of the board it is on.
Winning the game:
You win the game if you checkmate your opponent or your opponent resigns.
Stalemate:
The game is a tie (stalemate) if both players agree to a draw, a player cannot move on his turn, or if the board is in the exact same arrangement three times.
Did I miss anything?
-- Vilkacis