Mate in one, two, three
Mate in one
One move ends it. These are where every player starts, and they are worth coming back to: the mating pictures you can see instantly are the ones you will spot three moves away in a real game, and there is no way to build that library except by meeting the shapes over and over.
How to spot it
Look at the king's escape squares first, not at your own pieces. A king with one flight square needs a check that covers it; a king with none needs any check that cannot be captured or blocked. Working from the king outwards is faster than trying every check you have.
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.Qxg7#
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2. White to play Play it out →Answer
9.Qxf7#
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3. White to play Play it out →Answer
45.Rh7#
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4. Black to play Play it out →Answer
13...Qxh2#
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5. White to play Play it out →Answer
26.Qe6#
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6. White to play Play it out →Answer
26.Qxg7#
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7. White to play Play it out →Answer
35.g3#
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8. Black to play Play it out →Answer
25...Qa4#
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9. Black to play Play it out →Answer
16...Qxg3#
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10. Black to play Play it out →Answer
50...h2#
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11. White to play Play it out →Answer
16.Qd8#
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12. Black to play Play it out →Answer
11...Qf1#
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.