Collecting all the fish, bugs, and sea creatures is a core, ongoing activity in Animal Crossing: New Horizons. Each critter has specific spawn conditions (time of day, season, location, weather). Donate the first of each to Blathers at the museum to expand its collection. Selling duplicates is a great way to earn Bells.
Fish
Use a fishing rod near shadows in rivers, ponds, and the ocean. Different fish appear in different bodies of water and at various times. Pay attention to the size of the shadow.
Bugs
Use a net to catch bugs. They can be found on trees, flowers, rocks, on the ground, or flying in the air. Some require specific conditions, like rain or rotten turnips.
Sea Creatures
Equip a wetsuit and dive into the ocean. Look for bubbles rising to the surface, then dive down to catch the shadow. Some sea creatures move faster than others.