Tactics
The Greek gift
The bishop takes on h7 with check, the king takes the bishop, the knight comes to g5 with check and the queen arrives on h5. It is the oldest named attacking pattern in the game, it comes up in half the openings ever played, and it works on h2 for Black in exactly the same way.
How to spot it
The setup is a bishop aiming at h7, a knight ready to reach g5, a queen with a path to h5, and no black knight on f6 to cover it. Check those four things before you calculate anything, because when one of them is missing the sacrifice is usually just a lost bishop.
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
14.Bxh7+ Kxh7 15.Rh3+ Kg8 16.Qh5
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2. White to play Play it out →Answer
14.Bxh7+ Kxh7 15.Qh5+ Kg8 16.Ng5 Qxg5 17.Qxg5
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3. Black to play Play it out →Answer
14...Bxh2+ 15.Kxh2 Qh4+ 16.Kg1 Ng4 17.Qxg4 Qxg4
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4. White to play Play it out →Answer
12.Bxh7+ Kxh7 13.Rh3+ Kg8 14.Qh5
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5. White to play Play it out →Answer
9.Bxh7+ Kxh7 10.Qh5+ Kg8 11.Ng5 Qxg5 12.Qxg5
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6. White to play Play it out →Answer
16.Bxh7+ Nxh7 17.Qh4
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7. White to play Play it out →Answer
20.Bxh7+ Kxh7 21.Rh5+
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8. White to play Play it out →Answer
15.Bxh7+ Kxh7 16.Qh5+ Kg8 17.g6 Rxf4 18.Qh7+ Kf8 19.Qh8#
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9. White to play Play it out →Answer
7.Bxh7+ Kxh7 8.Qh5+ Kg8 9.Ng5
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10. White to play Play it out →Answer
15.Bxh7+ Kxh7 16.Qh5+ Kg8 17.Rf3 Bxg5 18.fxg5
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11. White to play Play it out →Answer
26.Bxh7+ Kxh7 27.Rh3+ Kg8 28.Rh8#
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12. White to play Play it out →Answer
19.Bxh7+ Nxh7 20.Ne7+ Kh8 21.Rxh7+ Kxh7 22.Rh1#
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.