Double attacks by the queen, like all others, have certain repeating characteristics that follow from the value of the piece and the types of moves it can make. Every chess player knows to value the queen because of all the different ways it can move. As students of tactics in general and double attacks in particular, however, we can see the queen’s value more precisely: purely as a matter of geometry, the queen can attack any two squares on the board at the same time; if you put the enemy king on one square and another enemy piece on another square, there is always a third square from which your queen can, in principle, attack them both. (In the skeletal diagram to the left, White’s queen forks Black’s king and rook.) We say “in principle” because often the needed square will be unreachable or protected, or the lines from the square to the king and loose piece may be blocked by other pieces. But it is worth reflecting anyway on this feature of the queen’s power. It helps explain why the queen surpasses all other pieces as a tactical weapon. As a double attacker it has no peer.
The queen’s immense usefulness also limits its power in this respect: it generally is too valuable to trade for any other enemy piece on the board. Of course the queen sometimes may be sacrificed to achieve checkmate; you may exchange queens, if the other is more dangerous than yours; and very occasionally you may give up your queen in return for a large number of your opponent’s other pieces. But usually it isn't worthwhile to use your queen to take an enemy piece that is protected. Either the protection has to be eliminated or a different, loose target has to be found. Notice the practical implication: usually at least one loose (i.e., unguarded) enemy piece must be found or created for a queen fork to be effective. This principle—the requirement of a loose piece—does not apply to knight forks, because if a knight attacks a rook or queen it makes no difference whether they are defended; you gain just by exchanging, because knights are less valuable than those other pieces.
We can go farther. When your queen inflicts a double attack, the enemy will have time to move one of the attacked pieces; if neither of them are his king, he usually will move whichever is unprotected. That means that to be effective a double attack by the queen usually has to attack either two unprotected pieces or an unprotected piece plus the king; for only then will there still be an unprotected piece left behind for your queen to capture after your opponent moves the more valued or vulnerable target of the fork to safety. Attacking the king here has all the advantages that it did when we studied knight forks: the opponent must attend to the threat, usually by moving the king or interposing something, thus leaving the other piece being forked to get taken. (An additional possibility we will consider, almost as good as attacking the king, is threatening mate. This less often is an issue for the knight than for the queen, because the knight less easily can make such threats.)
Here, then, are the key points to guide your hunting: the targets for a double attack by a queen usually include (a) the king—either by a check or by a mating threat, and (b) an unprotected knight, bishop, or rook. You are looking for squares from which your queen can attack two of those targets, or where it might be able to attack them after some preliminary maneuvers. From this we can deduce a fairly manageable set of challenges to making queen forks work: the forking square is guarded; the line to the forking square is blocked, or the line from the forking square to one of the targets is blocked; the king is not yet in position to be checked, but can be brought into position; there is not yet a loose piece at the other end of the fork, but a piece there can be loosened or an already loose piece can be forced there by threat or attraction. In the next sections we will study how to identify and solve each of these problems. The solutions to most of them involve exchanges.