Tactics
The fork
A fork is one piece attacking two things at once. Your opponent can answer one threat on their move and not both, so the second one is yours. It is the first tactic anybody learns and it never stops being the most common way material changes hands, at every level there is.
How to spot it
Look for enemy pieces that stand a knight's move apart, or on the same diagonal, or on the same rank with nothing between them. Then ask which of your pieces can reach the square that sees both. The king counts as one of the two targets and is the reason a fork with check is so often decisive: the answer is forced.
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
51...g1=N+ 52.Kf2 Nxe2
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2. Black to play Play it out →Answer
16...Nxf3+ 17.Rxf3 Qxe1+
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3. Black to play Play it out →Answer
28...Nd3+ 29.Kc2 Nxe1+
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4. Black to play Play it out →Answer
9...Qa5+ 10.Kf1 Qxb5+
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5. White to play Play it out →Answer
22.Nd4+ Kd6 23.Nxc2
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6. White to play Play it out →Answer
29.Rxg7+ Kf8 30.Rxf7+ Qxf7 31.Bxf7
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7. White to play Play it out →Answer
32.Rd8 Qxd8 33.Nf7+ Kg8 34.Nxd8
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8. Black to play Play it out →Answer
34...Ng5+ 35.Kg4 Nxe6+
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9. Black to play Play it out →Answer
27...Qf5+ 28.Kd4 Qxd5#
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10. White to play Play it out →Answer
10.Qxd8+ Nxd8 11.Nxc7+ Kf8 12.Rxd8#
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11. White to play Play it out →Answer
28.Qxe5 Rxe5 29.Nd3 Rxc2 30.Nxe5
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12. White to play Play it out →Answer
32.Nf6+ Kh8 33.Qxh6+ Bxh6 34.Rh7#
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.