Tactics
The overloaded piece
A piece defending two things at once is doing a job it cannot finish. Take one of them and the other falls, whichever way they recapture. Nothing has to be sacrificed and nothing has to be forced: the position is already lost for them, and the tactic is noticing it.
How to spot it
Count defenders rather than attackers. Any enemy piece appearing twice in your count is overloaded, and the move is to cash in the cheaper of its two duties first. Queens and rooks defending along a rank are the usual culprits, and so is a king who is the only guard of two squares.
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
24.Qf7+ Kh8 25.Qxf8+ Rxf8 26.Rxf8#
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2. Black to play Play it out →Answer
25...Re2+ 26.Kxe2 Qxc3
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3. White to play Play it out →Answer
23.Ne7+ Kh8 24.Nxf7+ Rxf7 25.Rd8+ Ne8 26.Rxe8+ Rf8 27.Rxf8#
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4. Black to play Play it out →Answer
24...Qxc2+ 25.Ke1 Bh4+ 26.Kf1 Qxd1+
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5. Black to play Play it out →Answer
26...Nh2+ 27.Kg1 Rxe1+ 28.Kxh2 Rh1#
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6. White to play Play it out →Answer
18.Qxc6+ bxc6 19.Bxa6#
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7. Black to play Play it out →Answer
21...Qc3+ 22.bxc3 Bxa3#
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8. White to play Play it out →Answer
32.f3+ Kh5 33.exf5
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9. White to play Play it out →Answer
10.Qxd8+ Nxd8 11.Nc7+ Kf8 12.Rxd8#
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10. White to play Play it out →Answer
33.Qc8+ Rxc8 34.Nd7+ Ka8 35.Rxc8#
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11. Black to play Play it out →Answer
27...Qf2+ 28.Rxf2 Rb1+ 29.Rf1 Bd4+ 30.Kh1 Rxf1#
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12. White to play Play it out →Answer
23.Qxh6+ gxh6 24.Nxf6+ Kh8 25.Rxg8#
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.