How can various structures on an organism give you clues to their environment or behavior?

Any evolutionary biologist will tell you that there are so many ways. The structures of an animal reflect their adaptations to their environment and their common behaviors. According to evolutionary theory, animals are born with genetic mutations that cause minor differences between animals. If these differences help the animal to survive and out-compete other animals, then they will become more fit to reproduce and have offspring to pass down their beneficial traits. Over time, the most beneficial traits will become fixed in a population--that is, every organism of a certain species in a certain environment will have that trait.

The structure of bird beaks is an Excellent example for this question. As Darwin observed, birds have various types of beaks that work best for the foods they eat. Some beaks are for insects, some for seeds, some for worms, while others are long and skinny for extracting nectar. Some are spoon-like for scooping up fish. To put this into context, imagine a bowl of gummy worms. If you try to pick up a worm with a spoon "beak" you will find it very difficult. However, if you had a pair of tweezers, you could pick up the worms very efficiently. Thus, a bird with a "tweezer" beak will be more fit since it can out compete other birds for its food source--worms. This is similar to how paleontologists distinguish between herbivores and carnivores in dinosaur fossils. Pointy teeth are suited for killing prey and ripping meat, while flat teeth are suited for grinding leaves.

Camouflage is another example. The color of an organism usually help it survive or reproduce in some way. Peppered moths, for example, come in dark and light shades. Their environment is the forest. Prior to the Industrial Revolution in England, the amount of light moths were much greater that the amount of dark ones because the tree bark was light. However, the smoke and soot from the Industrial Revolution darkened the trees, and the moths all became dark. This was because the dark moths hid well and so escaped predators while the light ones were unsuited for the new environment.

The examples are endless. Almost every animal structure has a purpose.