I think a good example of how animals/plants change form can be seen by looking at how we selectively grow crops and breed animals. We force them to evolve in ways that benefit us, so obviously it is not the same as natural selection, but it demonstrates how preferential breeding changes the form of living organisms over time. In nature this preferential breeding is determined by the natural advantages given to an organism. If a predator was born with a mutation that gave it slightly longer claws and those claws helped it catch more prey it is less likely to starve. Not starving would give it more opportunities to breed. If it breeds a handful of times and a couple of its offspring have the same mutation that gives the same advantage those offspring would also be more likely to be successful hunters and breed more times.
For a prey animal a random mutation might help them defend against a predator. Being better at not getting eaten would give them more opportunities to breed. Some of their offspring would have the same mutation that gave their parent a better chance at survival and they would also escape more predators and breed more times. The same thing goes for plants that get eaten by herbivores. Slowly the beneficial mutation is worked into the genetics of the species through natural selection and the appearance of the animal changes. It's very much common sense when you think about it and actually understand how the process works.
We "see" evolution all the time.
Insects developing a resistance to pesticides is an example of evolution.
People who do not believe in evolution will call that "adaptation", but that's not correct. Insects can't adapt to pesticides that kills them, but those that the pesticides don't kill precipitate and/or promote a change in the species driven by the fact that whatever genetic trait they posses which helps them survive becomes a dominant trait in the species as the members of the species lacking that trait are exterminated by the pesticides that they lack the genetic structure to survive.
That's not adaptation, that's evolution.
To wit.
Adaptation involves short-term changes to suit the habitat and environment.
Evolution is a long-term process wherein changes occur in the genetic level for a better functioning and survival as a race/species.