When your opponent’s king is checked he has three possible replies: move the king, capture the attacker, or interpose something between them. The last two frequently are impossible, which is why checks often can be used to push a king around, and which helps explain why the king makes an ideal middle piece in a skewer: often it has to move out of the way when attacked, exposing whatever is behind it to capture. And this same principle also means that even if the king doesn't appear to be in position to be skewered, you may be able to push it into position with a preliminary check or several of them. In addition to improving your ability to create skewers, these next studies thus will sharpen your ability to see not just what checks you can give, but what checks you will be able to give a move later—and then a move after that.
We'll start with cases where a single check pushes your opponent's king into position to be skewered. In this first simple position, each side has a king and a rook. Black would mate with Rh8 if it were his turn, but instead White has the move. At a time like this one must operate with checks that hold the initiative. How many checks does White have to consider? Only one: Ra6. White's rook can’t be captured and there is nothing to interpose, so Black has to move his king. Notice that White’s king attacks the three squares on the seventh rank where Black’s king might like to go; with those off limits there is nowhere for Black to move his king but the fifth rank (to c5, d5, or e5). Naturally you see now that Black's king and rook are aligned: White thus plays Ra5+, again forcing Black’s king to change ranks (perhaps back to its original position), and then comes RxR, ending Black’s mating threat and winning the game.