Tactics
Castling as a tactic
Castling moves two pieces at once, and there are positions where the second one is the point: the rook arrives on d1 or e1 with a threat, or the king steps out of a check that was about to be a discovered attack. It is easy to miss because it does not look like a candidate move.
How to spot it
Include castling in your list of checks and threats, especially castling long, which puts a rook on d1 or d8 where an enemy queen so often sits. Also worth remembering in reverse: a king that has moved cannot castle, so a check that forces the king to step is worth more than the tempo it costs.
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
12.Qxd8+ Kxd8 13.O-O-O+
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2. Black to play Play it out →Answer
15...O-O-O#
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3. White to play Play it out →Answer
23.Qxf5 Qxb2 24.O-O
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4. White to play Play it out →Answer
19.Ra8+ Ke7 20.Rxh8 Qxb4 21.O-O
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5. Black to play Play it out →Answer
8...Qxd1+ 9.Kxd1 O-O-O+ 10.Ke2 Nxe5
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6. Black to play Play it out →Answer
15...bxc3 16.Re1 O-O
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7. White to play Play it out →Answer
11.Nxe4 dxe4 12.Qb5+ Qd7 13.Qxe5 O-O-O 14.O-O
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8. White to play Play it out →Answer
16.O-O-O Rhd8 17.Nd5+ Kf8 18.Nxb4
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9. White to play Play it out →Answer
12.O-O d6 13.Bh6+
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10. Black to play Play it out →Answer
15...Qxd2+ 16.Kxd2 O-O-O+ 17.Ke3 Kxb7
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11. Black to play Play it out →Answer
10...Qxd5 11.Nxd5 O-O-O 12.Bc3 Rxd5
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.