Tactics
The hanging piece
A piece defended by nothing. Most games below master level are decided by one of these being left somewhere for a move too long, and the reason is never that the player could not see it: it is that they were looking at their own plan when the piece became loose.
How to spot it
The habit worth building is mechanical and takes two seconds: after every enemy move, name every one of their pieces that nothing defends. Then check whether any of them is attacked or can be attacked with tempo. Loose pieces are also what make forks and skewers possible, so this scan finds more than free material.
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
19.Rxf8#
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2. White to play Play it out →Answer
31.Qxe8+ Rf8 32.Qxf8#
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3. White to play Play it out →Answer
19.Qxa8+ Qb8 20.Qxb8+
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4. White to play Play it out →Answer
21.Nxe7+ Kh7 22.Rh4#
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5. Black to play Play it out →Answer
19...Bxa6 20.Qxa8 Bxf1
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6. White to play Play it out →Answer
29.Qxe8+ Kg7 30.Qxe5+
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7. Black to play Play it out →Answer
10...Nxe4 11.Qxd8 Bxd8
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8. Black to play Play it out →Answer
16...Qxc3 17.Bd2 Qxd4
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9. White to play Play it out →Answer
14.Qxc6+ Bd7 15.Qxd5
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10. Black to play Play it out →Answer
13...Qxc3 14.d4 Qxb4
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11. White to play Play it out →Answer
19.Rxe2 Rd1+ 20.Re1 Rxb1 21.Rxb1
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12. Black to play Play it out →Answer
34...Qxe6 35.Qxe3 Qxc6
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.