Tactics
The defensive move
Not every puzzle is a win. These are positions where you are being mated or losing a piece, and exactly one move survives. They are worth more practice than they get: games are lost by missing the defence far more often than they are won by finding the brilliancy.
How to spot it
Find the threat first, in words, before looking for moves. Then there are only four answers to any threat: take the piece making it, block the line, move the target, or make a bigger threat of your own. Going through those four in order finds the move much faster than staring at the position does.
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
74.g7 Rc8 75.Bf8
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2. Black to play Play it out →Answer
61...Kf7 62.Ke4 d2
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3. White to play Play it out →Answer
61.Kb7 Kd4 62.a7
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4. White to play Play it out →Answer
37.Bxe5 Rc1 38.Rxf6+ Kh7 39.Rf7+ Kg8 40.Rg7+ Kf8 41.Rg1
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5. Black to play Play it out →Answer
15...Bb4+ 16.Kd1 O-O
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6. Black to play Play it out →Answer
40...Ra6+ 41.Re6 Rxe6+ 42.Kxe6 e4
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7. White to play Play it out →Answer
45.h7 Rh1 46.Rd8
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8. White to play Play it out →Answer
27.Rxe4 dxe4 28.Qxc7 e3 29.Qg3
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9. White to play Play it out →Answer
50.f4 Rxg6 51.e8=N+ Kf7 52.Nxd6+
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10. White to play Play it out →Answer
35.bxc4 bxc4 36.Kh5
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11. Black to play Play it out →Answer
26...Kf8 27.Qxb8 Rxb8
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12. Black to play Play it out →Answer
46...hxg3 47.a8=Q f2+ 48.Ke2 Bc4+ 49.Kxe3 f1=N+ 50.Ke4 Bd5+ 51.Ke5 Bxa8 52.hxg3 Bd5
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.