Mate in one, two, three
Mate in three
Three moves is where mating puzzles stop being pattern recognition and start being calculation. It is also where the answer starts being a move that is not a check, because at this length there is time to take an escape square away first and mate afterwards.
How to spot it
Checks first, since most of these are forcing throughout, but when every check fails, stop looking at checks. Ask what their king would need to be able to do to survive, and find the move that removes it. Then recount, because a quiet move gives them a free move too.
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
44.Qg5+ Kf7 45.Qg7+ Ke6 46.Qxe7#
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2. White to play Play it out →Answer
28.Rd7+ Bxd7 29.Rxd7+ Ke8 30.Qxg8#
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3. Black to play Play it out →Answer
26...Rxf2+ 27.Rxf2 Qg3+ 28.Kf1 Qxf2#
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4. Black to play Play it out →Answer
39...Rh2+ 40.Kg4 Re4+ 41.Kf3 g4#
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5. Black to play Play it out →Answer
42...Nf3+ 43.Kh1 Qb1+ 44.Rc1 Qxc1#
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6. White to play Play it out →Answer
43.Rg7+ Kh6 44.Nf5+ Kh5 45.g4#
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7. Black to play Play it out →Answer
28...Qf2+ 29.Kc1 Qf4+ 30.Qe3 Qxe3#
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8. Black to play Play it out →Answer
44...Qf2+ 45.Kh3 Qf3+ 46.Kh4 Qxg4#
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9. White to play Play it out →Answer
21.Qf7+ Kh8 22.Qe8+ Nf8 23.Qxf8#
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10. Black to play Play it out →Answer
50...b5+ 51.Kxb5 Rb1+ 52.Kc4 Rb4#
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11. Black to play Play it out →Answer
22...Qg1+ 23.Rxg1 Rxh2+ 24.Bxh2 Nf2#
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12. White to play Play it out →Answer
35.Re8+ Bxe8 36.Nf6+ Kh8 37.Rh7#
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.