Tactics
The kingside attack
Both sides usually castle short, so most attacks happen on the same three files, and the same handful of ideas keep working: the bishop sacrifice on h7, the knight arriving on f5 or g5, the rook lift, the h-pawn coming down the board.
How to spot it
Look at the pawns in front of their king. A pawn that has moved is a square that cannot be defended by a pawn again, and every attacking idea aims at exactly those squares. Then bring the pieces that are not yet doing anything: attacks fail from being one piece short far more often than from being unsound.
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. Black to play Play it out →Answer
14...Qxh2#
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2. Black to play Play it out →Answer
40...Nh3+ 41.Kh1 Nxf2+
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3. White to play Play it out →Answer
22.Rh8+ Bxh8 23.Qh7#
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4. White to play Play it out →Answer
26.h7+ Kxh7 27.Rh4+ Rh5 28.Rxh5+ gxh5 29.Qxh5+ Kg8 30.Qh8#
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5. Black to play Play it out →Answer
22...Rxh2+ 23.Bxh2 Rxh2+ 24.Kxh2 Qh7+ 25.Qh6 Qxh6#
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6. White to play Play it out →Answer
23.Re8+ Rxe8 24.Rxe8+ Bf8 25.Bf6#
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7. White to play Play it out →Answer
16.Qh6+ Qh7 17.Qxf6+
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8. Black to play Play it out →Answer
11...Qxf1+ 12.Kxf1 Ba6+ 13.Qd3 Bxd3+
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9. White to play Play it out →Answer
24.Bf6+ Bg7 25.Ng6#
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10. White to play Play it out →Answer
26.Qxf6+ Rxf6 27.Rg8#
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11. Black to play Play it out →Answer
17...Qg1+ 18.Rxg1 Rxh2+ 19.Bxh2 Nf2#
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12. Black to play Play it out →Answer
24...Nf3 25.Qxd6 Qxg2+ 26.Rxg2 Rf1+ 27.Rg1 Rxg1#
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.