While some of the rules of the game are not known for certain, we can make good assumptions about how the game was played based on the Persian descendant, Shatranj, which was believed to have very similar rules. As such, we will use the Persian names for the pieces.
Objective
Deliver Shah Mat to the opponent's Shah, deliver stalemate to the opponent's Shah, or capture all the opponent's pieces.
Turns
The player with the white pieces makes the first move, then the two players alternate taking turns.
Board
The game is played on an 8x8 grid. Each square may be occupied by a maximum of one piece. During a turn, a player moves one piece from its present position to another square. Players may not choose to skip their turn. If a player cannot make a legal move, it is stalemate and they lose the game. If a player moves a pieces to a square occupied by an opposing piece, that piece is removed from the board and replaced with the player's piece. This is called capturing.
Starting position
White's first rank is set up with chariot, knight, alfil, shah, ferz, alfil, knight, chariot. White's second rank is set up with all pawns. Black's position is setup exactly like white's on the seventh and last ranks, with the shahs facing each other.
Piece movement
The Shah moves one square in every direction. If the shah is attacked by an opposing piece, it is in check. The shah must move away from the attack, capture the piece attacking the shah, or block the checking piece with an allied piece. The shah may not move into a square that is attacked by an opposing piece. If the shah is in check and cannot escape check, then it is shah mat and the player loses the game.
The Ferz moves one square diagonally in every direction.
The Alfil moves two squares diagonally in every direction. The alfil can jump over other pieces to move or capture. The alfil cannot move just one square.
The Knight moves two squares orthogonally, and then one square perpendicularly in every direction. The knight can jump over other pieces to move.
The Chariot moves any number of squares orthogonally in every direction, but cannot move or capture by jumping over other pieces.
The Pawn moves one square forward and captures one square diagonally to either of the squares in front of it. The pawn promotes to a ferz once it moves to the last rank. The pawn must be promoted, it cannot be left on the last rank as a pawn.