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The Chess Game grail being the CheckMate of the Nemesis' King. 

The Chess Match is played on an 8x8 Grid with alternating colored squares which are laid out in a checkered (chequer) pattern in light and dark squares.

The Chessboard is a square board that is divided into eight rows (Hortizontal lines) of squares called Ranks.  And eight columns called Files (Vertical lines), with a light-colored square in each player's lower Right Corner. Diagonal Lines are at 45 degrees.

The Chess Match is played with 32 total pieces.  Positioned on each side the Playing Board, there are 16 pieces. On the Chessboard, there are 6 distinct pieces.  Five of the 6 distinct pieces have Linear Movements.  Only, The Knight has Circular Movements.

The Chess pieces on each side of the Chessboard are one King, one Queen, two Rooks, two Bishops, two Knights, and eight Pawns.  The Chess pieces are usually White and Black.

Each Chess piece has its own way of moving around the Chessboard.  The Chess pieces will be postioned to: Advance, Capture and to CheckMate the Nemesis's King.  These pieces may assume a board postion of a captured piece.  See Diagram:  The lower case "m" marks the squares, where the individual piece may move.  Chess pieces may not move to a square occupied by a piece of the same color.

The King:

Moves one square in any direction (except, when Castling).  The King may not move to any square where he is placed in Check by an offensive piece. However, The King may move to a square that is occupied by an opponent's piece and capture said piece, and remove it off the Chessboard.

The Queen:

Moves in any direction on the ranks, files, and diagonally.  The Queen captures an opposing piece by landing on its square. 

The Rook:

Moves in any distance on the ranks or files (liken to a letter T) and The Rook captures an opposing piece by landing on its square.

The Bishop:

Moves in any diagonal distance (liken to an X shape), always remaing on the same color of square.  The Bishop captures an opposing piece by landing on its square.

The Knight:

Moves in a manner liken to an "L" shape.  Each move must be either two squares along a rank and one square along a file.  Or two squares along a file and one square along a rank.  The Knight captures an opposing piece by landing on its square.  The Knight is the only piece that may Leap over any other pieces.

The Pawn:

Moves only forward on the board.  On the first move, Pawns may move either one or two squares forward.  The Pawn captures, moving diagonally, only one square.  Not as it moves foreward.  Further, see Pawn Movements Diagram and En Passant Rule.

En Passant Rule:  Pawn captures an opposing Pawn.

An opponent's Pawn must be on the 5th rank from its side, to avail of the En Passant Rule.  When a Pawn moves forward two squares past an opposing Pawn on an adjacent file the En Passant maneuver is made accessible.  The opponent's Pawn may capture the double-mover Pawn as if this Pawn had moved forward one square.  This option is only open, during the offensive Kingdom's (Pawn) next move. The En Passant coda keeps the Chess Match, more open.  Further, see Pawn Movements Diagram.  En Passant means in Passing, in French.

When a Pawn reaches the defensive King’s Row, it must be promoted to either:  The Queen,  The Bishop, The Knight, or The Rook of the same color (offensive player's option).  The Pawn is usually promoted to Queen.  In various advantageous cases, an alternative piece is chosen to replace The Pawn, called 'under-promotion'.

When players wish to adjust a piece on the board, they must first say "J'adoube" (I adjust) or the equivalent. Otherwise, if a piece is touched, it must be moved (when possible).  This is the 'Touch and Move' Rule.   If no legal move is possible with the touched piece, the player makes a legal move with another piece.

When a player's hand leaves a piece after moving it.  The move is complete and may not be changed (unless, the move was not legal).

Agreed Draw:

The Chess Match may end in a Draw at any time.  If one player offers a Draw and the Nemesis accepts.  Draw has now occurred.

Insufficient Material or Dead Position:

A position where no series of legal moves would lead to a Checkmate. The Chess Match ends.  Draw has now occurred.

Stalemate:

If a player cannot make a move, and the player's King is not in Check. Draw has now occurred.

50 Move Rule:

The Chess Match will End in a Draw, if no piece is captured after fifty moves. Draw has now occurred.

Three-Fold Repetition:

If the same movement is repeated three times during a Chess Match (with the same player moving each time).  The player next to move may claim a Draw.  Draw has now occurred.

CheckMate:

When the defensive King is in Check and cannot move out of Check.  CheckMate.

Resignation:

A player may resign at anytime, usually because the game position is hopeless.  A losing player resigns by placing their King on its side.

Out of Time:

When the Player's Clock Time is over (exceeding the Time Control).  This is not the Rules of the Chess Match, but part of the Chess Rules (where Chess Clocks are used).

The Rules of Chess are governed by the World Chess Federation, known by the initials FIDE, meaning Fédération Internationale des Échecs.  The rules are in the section Rules of Chess of the FIDE Handbook.  FIDE also offers Rules and Guidelines for Chess Tournaments.