The actual rules, for anyone starting from zero.
Chess is played on an 8×8 board of alternating light and dark squares, with the board positioned so each player has a light square in their bottom-right corner. Each side starts with 16 pieces: one king, one queen, two rooks, two bishops, two knights, and eight pawns. White always moves first, and players alternate turns from there.
King: One square in any direction — horizontally, vertically, or diagonally. The king can never move into a square attacked by an enemy piece.
Queen: Any number of squares in any direction — horizontal, vertical, or diagonal — as long as nothing blocks the way. It's the most powerful piece on the board.
Rook: Any number of squares horizontally or vertically, but not diagonally.
Bishop: Any number of squares diagonally. Each side's two bishops stay on their starting color for the whole game — one travels only on light squares, the other only on dark squares.
Knight: Moves in an "L" shape — two squares in one direction, then one square perpendicular to that. The knight is the only piece that can jump over other pieces in its path.
Pawn: Moves straight forward one square, or two squares from its starting position. Pawns capture differently from how they move — diagonally, one square forward. A pawn can never move or capture backward.
When a king is directly threatened with capture, it's in check, and the player must immediately do something about it — move the king to safety, block the attack with another piece, or capture the attacking piece. If none of those options exist, it's checkmate, and the game ends immediately.
If the player to move has no legal moves available but their king is not in check, that's a stalemate — the game ends immediately as a draw, regardless of how much material either side has left. Games can also end in a draw by mutual agreement, by threefold repetition (the same position occurring three times), by the 50-move rule (50 moves without a pawn move or capture), or by insufficient material for either side to deliver checkmate.
Castling: A king and rook can move together in one special move — the king moves two squares toward the rook, and the rook jumps to the square the king passed over. This is only legal if neither piece has moved yet this game, there are no pieces between them, and the king isn't in check, doesn't pass through check, and doesn't land in check.
En passant: A special pawn capture. If an opponent's pawn moves two squares forward from its starting position and lands directly beside your pawn, you may capture it as though it had only moved one square — but only on the very next move, or the option disappears.
Promotion: When a pawn reaches the far end of the board (the 8th rank for White, the 1st for Black), it must immediately be exchanged for a queen, rook, bishop, or knight of the same color — almost always a queen, since it's the strongest piece.
Once the rules feel natural, Chess Opening Principles covers what to actually do with your first few moves. Or jump straight into a game on Play.