What is Chess?

Chess is a game played by two players, who we'll call White and Black. It is played on a board of 64 squares. Each square can be empty or occupied by a piece. The initial position of the game consists of 16 white pieces and 16 black pieces, arranged as shown in the following diagram.

Players alternate making moves. White always goes first. In a typical move, White selects a white piece and moves it to another square. The destination square is either empty or occupied by an enemy piece. In the latter case the enemy piece is said to be captured. The captured piece is removed from the board, and plays no further role in the game.
Looking across the bottom row of white pieces we see a rook (sometimes called a castle), a knight, a bishop, a queen, a king, another bishop, another knight, and another rook. The next row of white pieces consists of eight pawns. Each different type of piece moves in a specific way, as described in detail in the rest of this tutorial.
The goal of the game is to capture the opponent's king. However to actually capture the king would be offensive. So this is not allowed. This leads to the notion of check. Black's king is said to be in check if (assuming it were White's turn to move) White could capture Black's king. To avoid this capture, Black must make a move that takes Black's king out of check, so White cannot capture Black's king on the next move.
If it's impossible for Black to get out of check, then Black's king is said to be checkmated, and White wins the game. Another way to describe checkmate is to say that Black is in check and Black has no legal moves. An alternative outcome is if Black is NOT in check but has no legal moves. This is called a stalemate. When this occurs the game ends in a draw.
The remainder of this tutorial explains how all the pieces move, and a few other rules that don't quite fit the pattern described here, such as castling, promotion and en passant. These notes only try to explain the rules. Learning to play well is a different story.