Tactics
Deflection
A piece is doing a job, holding a square, guarding a mate, defending a rook. Deflection makes it an offer it cannot refuse somewhere else, and while it is away the thing it was defending falls. Usually the offer is a capture it has to take, which is why so many deflections start by giving something away.
How to spot it
Work out what is defending the square you want, then ask what would make that piece leave. This is the tactic that most rewards asking the question backwards: start from the mate or the win you *would* have if a single enemy piece were elsewhere, then find the move that sends it there.
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
31.b7 Rxb7 32.Rxc8+
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2. Black to play Play it out →Answer
27...Bh2+ 28.Kh1 Rxf1#
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3. White to play Play it out →Answer
34.Qg6+ Qg7 35.Qxe6+
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4. Black to play Play it out →Answer
37...Rh1+ 38.Kxh1 Qxg3
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5. Black to play Play it out →Answer
23...Qe2+ 24.Kg1 Qxe1+ 25.Rxe1 Rxe1#
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6. Black to play Play it out →Answer
21...Qxc3+ 22.bxc3 Bxa3#
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7. White to play Play it out →Answer
14.Qc8+ Qd8 15.Bxf7+ Kxf7 16.Qxd8
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8. White to play Play it out →Answer
26.Bd6+ Qxd6 27.Rb7+ Kc6 28.Rb6+ Kxb6 29.Qxd6+
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9. White to play Play it out →Answer
28.Rxf8+ Bxf8 29.Qf7+ Kd8 30.Qxf8+ Kd7 31.Qxa8
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10. Black to play Play it out →Answer
27...Rxh1 28.Rxh1 Nxg5
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11. Black to play Play it out →Answer
16...Na2+ 17.Bxa2 Rxc3+ 18.bxc3 Bxa3#
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12. Black to play Play it out →Answer
29...Qf1+ 30.Bd1 Qc4+ 31.Bc3 Be3#
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.