Here is a particularly famous and useful idea for achieving a smothered mate, first offered in 1497 by Juan Ramirez Lucena of Spain. White begins with 1. Qe6+, forcing Black’s king back to h8. Now White’s knight does a little dance: 2. Nf7+, Kg8; 3. Nh6++, which discovers check by the queen and thus keeps the knight safe on its new square. Black is forced to play 3. …Kh8 (if he tries Kf8 he gets mated right away with Qf7). Now: 4. Qg8+, forcing 4. …RxQ—and Black’s king is entombed in the corner. 5. Nf7 mates.

Notice two motifs worth mastering here: the sacrifice of the queen on g8, forcing Black to capture there and trap his own king; and the use of the knight first to push the king into the corner and then to give cover to the queen on g8 (and thus prevent Black’s king from capturing there itself).