We start with simple positions where the queen is one move away from inflicting a double attack. Even if you are new to queen forks you may be able to see the solutions to many of these right away. It’s still worth studying them methodically so that your grasp of the principles involved will be clear when we move to more complicated cases. For other readers double attacks with the queen may be hard to spot at first; in the beginning the board will look like a sea of pieces and squares, with the queen coming out of nowhere to attack two targets. But in fact most double attacks with the queen follow recognizable patterns, and these simple positions will enable you to nail down their fundamentals before worrying about how to remove obstacles to their execution.
In each position your task is to find a square your queen can reach and from which it will (a) check the enemy king and (b) attack a loose enemy knight, bishop, or rook. So you might begin by finding the undefended enemy pieces on the board. Think of this as a basic and ongoing part of your job during a game; every loose piece is a potential target you might be able to take for free with a double attack.
Next, look at any checks available to your queen. Sometimes this will be easy, but more spectacular double attacks often require you to notice checks possible from counterintuitive squares. It is good to be exhaustive. Think of it this way: the queen can move in both directions on the rank where it sits, on the file where it sits, and on each of the two diagonals where it sits. So it has a maximum of eight available paths. Be aware of its possible movements along each of them, asking if any squares it can reach would provide it with an open line to the enemy king—and whether any of those same squares also provide it with an open line to a loose enemy piece. In practice you can disregard some checks very rapidly, but as you are learning about forks you are better off erring on the side of being thorough.
The example to the left is as simple as the pattern gets. Again, you are looking for two things: unprotected (“loose”) Black pieces, and moves by White that check the Black king. The idea is to combine those ingredients to create a double attack. Black has one unprotected piece: the knight. White has one way to check the king: Qd8. That move also attacks, and collects, the knight after Black spends a move relocating his king to h7.