Does the knight move two steps forward and then to left or right or does it move one step forward and then diagonally to left or right? I was taught move one square then to right or left My partner says other way and we are fighting over it! Please can someone help.
Like everyone says, the two definitions are equivalent, but if you want an official-looking source, here is the quote from the USCF rulebook:
8E. The knight. The knight’s move is composed of two different steps. First, it makes one step of one single square along the rank or file on which it stands. It does not land on that square, as its move is not complete (9A). Then, still moving away from the square of departure, it moves one step of one single square on a diagonal. It does not matter if the square of the first step is occupied.
This move is sometimes called an L move, as it is equivalent to moving the knight two squares vertically, then one square horizontally (or two squares horizontally, then one square vertically). Note that the knight always moves to a square different in color than that of its starting square. A knight has a maximum of eight possible moves.
U.S. Chess Federation. United States Chess Federation's Official Rules of Chess, Sixth Edition (Kindle Locations 941-946). Kindle Edition.
There are yet more ways of looking at the knight's move. This one is from the FIDE handbook, and while clearly correct I don't think it reflects the way most people think of the move:
3.6 The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal.