Now consider a scenario opposite to the one we have been studying: you see a loose enemy piece you can attack, but not the other ingredient of a classic queen fork: a check you can give at the same time. You need to make the king move someplace where it can be attacked simultaneously with the loose piece. The most natural way to do this is with a preliminary check from a different piece or perhaps from the queen itself. The check forces the king to move, and once it reaches its new square a fork may follow. Another way to move the king is by initiating an exchange, rather than a check, that draws the king onto a square where it can then be attacked—or pushed around some more. The practical point: if you need to move the king, ask what checks you have and what the king protects that you might be able to capture; if the answers to those questions help move the king but not far enough, then ask them again.
In this first example to the left, White’s rook is loose; that is a starting point for analysis because it gives you a target to focus on. Ideally Black would like a move that attacks the rook and gives check at the same time. Presently it can't be done, so look for any checks that might force the White king into a position where it could be attacked along with the rook. It turns out that Black has just one such check to examine: Rd1. White is required to answer with Kh2. Now reassess the resulting board, again asking whether Black can attack the king and the loose rook at the same time. This time you find Qb8+, winning the rook.
The other route to the solution is to look first at Rd1. When your rook has a clear path to the enemy king's rank, it's natural to consider moving it there and to ask what the reply would be. Here you see that White's king escapes to h2. The crucial thing is to keep pressing then, asking what your next checks might be and whether any of them can be turned into forks.
This position is a nice study either way you look at it because the idea of a fork does not particularly suggest itself at the outset; it is not a case where there are visual clues indicating that the fate of White's king and rook are linked. Producing a crushing, game-winning fork in two moves thus might seem magical to the uninitiated. But the magic is the residue of method.