Tactics
The pawn fork
A pawn attacks two squares, and if two enemy pieces are standing on them the pawn wins one of them. Nothing on the board trades more cheaply: the defender can take the pawn only with something worth more than a pawn, which is every piece they own.
How to spot it
Look at enemy pieces standing two files apart on the same rank, then ask whether a pawn can reach the square between them, one rank behind. The push is often a sacrifice on its face, because the square is defended, and it works anyway: they can only capture with a piece and they still lose the other one.
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
41.e8=N+ Kg6 42.Nxf6
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2. White to play Play it out →Answer
62.g8=N+ Kf7 63.Nxh6+
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3. White to play Play it out →Answer
45.e8=N+ Kxf8 46.Nxd6
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4. White to play Play it out →Answer
92.b8=N+ Kd6 93.Nxc6 Kxc6 94.Kb8
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5. White to play Play it out →Answer
10.dxe5 Bxc2 11.Qxc2 Bxe5 12.Bxe5
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6. White to play Play it out →Answer
31.g4+ Kf4 32.Ne6+ Kxf3 33.Nxd8
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7. Black to play Play it out →Answer
20...exf2+ 21.Kxf2 Rd2+ 22.Kf1 Rxb2
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8. White to play Play it out →Answer
21.f4+ Kf6 22.fxe5+
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9. White to play Play it out →Answer
29.f4 Bxf4 30.Rxf4
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10. Black to play Play it out →Answer
19...fxe5 20.Nxc6 exf4 21.Nxd8 Bxa1 22.Rxa1 Rxd8
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11. White to play Play it out →Answer
47.f7 Bxf7 48.Qxh6+ Kg8 49.Nf6+ Qxf6 50.Qxf6
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.