It's like chess, only with a duck.
The duck occupies one square on the chess board at all times, and acts as a blocker. It cannot be moved through or taken, and the square it occupies is for the duck alone.
You move a chess piece, then move the Duck.
Every chess move must be followed by a Duck move.
The Duck can be moved to any square on the board.
So, a game might start:
1. e4/De6 (preventing 1...e5 and 1...e6)
1...c5/De2 (preventing developing of Queen or Bishop)
2...e6/De2 (as above)
A move is not complete until the duck has been moved.
The position after the duck has moved must be legal under Duck Chess rules, but can include things like:
The Black King was not and is not in check!
You win by taking the King (there is no 'checkmate' claim). Do announce checks, as the position must be legal.
Because the Duck can intervene, you will probably succeed in taking the enemy King only by moving next to the King first, or by using a Knight. The other way to win is by Zugzwang e.g. with bK on e8 between bRd8 and bBf8 and with, 1.Qe6/De7 will win as Black must move the Duck next move, exposing the King to the Queen's glare.
All other normal rules of chess apply.
We have recently invested in a modest quantity of small rubber ducks, all the better to play this game.
I don't know the author or anything else about this game, but I'd like to.