By difficulty
Easy puzzles
Two-move tactics, mostly. A capture or a check first, then the point. This is the band where most club players live and where the fastest improvement is available, because the patterns here are the ones that actually come up in your games.
How to spot it
Look at forcing moves in order: checks, captures, threats. Nearly everything at this level is found by that list, and the ones that are not are usually a defender being removed.
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
25.Qf8+ Rxf8 26.Rxf8#
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2. White to play Play it out →Answer
33.Qxg4+ Qxg4 34.Nxg4
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3. White to play Play it out →Answer
42.Rxh6+ Bxh6 43.Qxh6#
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4. Black to play Play it out →Answer
34...Rxd3+ 35.Bxd3 Rxd3#
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5. Black to play Play it out →Answer
6...Bf2+ 7.Ke2 Nd4#
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6. Black to play Play it out →Answer
20...Qxf2+ 21.Kd1 Qf1+ 22.Rxf1 Rxf1#
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7. Black to play Play it out →Answer
39...hxg6 40.hxg6 a2 41.Kf7 a1=Q
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8. White to play Play it out →Answer
19.Nd6+ Kb8 20.Nxf5
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9. Black to play Play it out →Answer
44...Qc2+ 45.Kg1 Qf2+ 46.Kh1 Qf1+ 47.Kh2 Rf2+ 48.Bg2 Qxg2#
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10. Black to play Play it out →Answer
28...Qxg2+ 29.Rxg2 Rc1+ 30.Rd1 Rxd1#
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11. Black to play Play it out →Answer
36...Rxf1+ 37.Rxf1 Rxf1+ 38.Kxf1 Qd1#
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12. Black to play Play it out →Answer
21...Nf3+ 22.Kh1 Rxh2#
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.