For fishes, it often varies wildly based on the species in question: what’s critical in one species is irrelevant in another. There are some basic rules of thumb, though:
-One of the more common ID characters in fishes is fin placement/position relative to other fins, and also being able to see telltale markings on the fins themselves. Make sure you can see where each fin begins and ends, gently extending them slightly if they sit flat. Very important for some species (differentiating some Atlantic sharks, and IDing goldeye vs. mooneye, are good examples)
-On the topic of fins, for some reason the dorsal and anal fins tend to be most important for ID, much more so than the other fins.
-For ray-finned fishes, best ID often needs an exact fin-ray count, often only seen if fins extended manually or if photographed in water, such as underwater or in a photo tank. Sand shiner vs. mimic shiner are most easily differentiated by anal-fin ray count of 7 vs. 8, which can be difficult on a tiny, panicked minnow in less-than-perfect light.
-For fish with scales, scale counts of the lateral line down the side of the fish can be crucial. Make sure when holding the fish, you avoid covering these side scales as much as possible if scales are an ID characteristic.
-Some fishes ID based around the head/mouth, such as mouth length relative to eye, the color of chin whiskers (bullheads), or mouth shape (redhorses).
-Sunfish (which I see/ID often on iNat) are best distinguished by the colored opercular flap behind the head, along with side patterning/coloration and pectoral fin shape.
-Overall, at least one good, unobstructed side view is crucial. Angles tend to distort the fish’s proportions and make it harder to ID. Best to take one of these photos with the fish laying flat or in a photo-tank.