• Castling. King moves two squares toward a rook, the rook hops to its other side. Only if neither has moved, the squares between are empty, and the king is not in check now, on the way, or at the end.
• En passant. If an enemy pawn jumps two squares and lands beside your pawn, you may capture it diagonally as if it had moved only one — but only on your very next move.
• Promotion. A pawn reaching the far end must become a queen, rook, bishop or knight. Pick the queen unless a knight gives immediate check or mate.

• Checkmate. The king is attacked and there is no legal move. That side loses.
• Stalemate. A player has no legal move but is not in check. It is a draw — a lifeline for the losing side, so watch for it when you are winning.
• Draw by material. Neither side has enough pieces to force mate (for example king and bishop versus king).
• Fifty-move rule. Fifty moves each with no capture and no pawn move.
• Repetition. The same position appears three times.

Each square has a name from its file letter and rank number. Moves are written as the piece letter plus the destination.

e4 pawn to e4  ·  Nf3 knight to f3  ·  Bxc6 bishop captures on c6
O-O castles kingside  ·  O-O-O queenside
+ check  ·  # checkmate  ·  e8=Q promotes to a queen

K=king, Q=queen, R=rook, B=bishop, N=knight (N, because K is taken). Pawns get no letter.

• Leaving pieces hanging. Before you release a piece, ask "can anything take this?"
• Bringing the queen out on move two. She gets attacked and you lose time developing.
• Forgetting the back rank. Once you have castled, make a small pawn move to give your king air.
• Grabbing every pawn. A pawn is rarely worth letting your opponent develop three pieces.
• Only looking at your own plan. After every opponent move ask what it attacks.