That puzzle is not about teaching your villagers to fish for food. It's about a special fish, and there are several requirements to solve it. In general, the best approach to solving puzzles on your own is to drag villagers around the island after every tech purchase, looking for new things that they can do. You should try it with several different villagers, because villagers with different skills will see different things. A scientist, for example, will notice things that a builder or farmer won't see, while a farmer will see things that the others will miss. Also, the more skilled your villager is, the more they will be able to see.
If you would like hints (or even the exact solution), you can check out the
Guides Section.