Alrighty. First I'll just try to remember some examples off the top of my head and look for articles to back me up later when I have more time.
Darwin came up with his theory after visiting the Galapagos Islands. The animals and plants on each island were unique to their respective island. They closely resembled the animals on mainland America but were different species. Mostly notably the finches on each island all had different beak morphology that best suited the types of plants available to them. Goes along with the survival of the species, yada yada...ok just a deduction.
Australia and Madagascar also boast animals completely unique to their islands, evolving from a much earlier common ancestor after they broke off during the continental shift.
We have vast fossil records to back up evolution. You can see how the skeleton structure of species change through time. There are prehistoric animals that bridge the gap between fish and amphibians and amphibians and reptiles and reptiles and mammals.
You have dinosaurs (who have bird-like features already such as air sacs), and then you have dinosaurs with feathers, and then birds. All neatly lined up in sedimentary rock showing the progression.
And with modern animals you can compare how closely related their DNA is in addition to their bone morphology and fossils and place where they came from.
Will also add this pic because I always found whale evolution to be cool/weird:
Oh yeah! Vestigial organs! .....sorry all over the place. Haven't read up on any of this stuff in years.