Mate in one, two, three
Mate in two
The first move does the work: it takes a square away, deflects a defender, or drags the king somewhere worse. Then it is mate whatever they do. This is the length at which calculation actually begins, because you have to check every one of their replies rather than only the one you expect.
How to spot it
Find the mating picture first and the move second. Decide what the position would have to look like for you to mate, then ask which single move makes it look like that. And when you have a candidate, check their best defence rather than their most natural one.
The positions
Easiest first. Every one is from a real game, and the rating under each board is what it costs the players who have tried it on lichess.
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1. White to play Play it out →Answer
16.Qe8+ Rd8 17.Rxd8#
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2. White to play Play it out →Answer
16.Bb5+ Kd8 17.Re8#
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3. Black to play Play it out →Answer
19...Qh4+ 20.Kf1 Qf2#
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4. Black to play Play it out →Answer
37...Qxf4+ 38.Kh3 Qg4#
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5. Black to play Play it out →Answer
43...Bh6+ 44.Kd1 Rc1#
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6. White to play Play it out →Answer
19.Rxg7+ Kh8 20.Rh7#
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7. Black to play Play it out →Answer
39...Qg2+ 40.Qg3 h5#
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8. Black to play Play it out →Answer
48...Rg1+ 49.Kh3 Rh8#
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9. Black to play Play it out →Answer
25...Qxf2+ 26.Kh1 Qf3#
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10. Black to play Play it out →Answer
47...Be6+ 48.f5 Bxf5#
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11. White to play Play it out →Answer
35.Rd5+ Rxd5 36.f4#
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12. Black to play Play it out →Answer
26...g5+ 27.Kxg5 Bh6#
Reading about a pattern is the easy half. Motify finds the positions where you missed one, by running your own lichess and Chess.com games through Stockfish, and puts each of them behind two or three puzzles on the same idea so you meet it having just found it three times. See how Motify works.
Positions from the lichess puzzle database, released under CC0.