I won't prove that evolution is what actually happened. I'm going to explain how it works. This because lots of times people don't understand it, or just have a wrong idea of it.
So, there are several points:
1- Each individual is different to the rest of the individual of its species/population (i.e. it has a different phenotype).
2- Some of this differences are hereditable.
3- Not all of the individuals from a population have the same survival probabilities, therefore, not all individuals survive to have progeny.
4- That progeny has the phenotype of their parents.
5- If a phenotype survives AND has more progeny (fitness), in a time, the other phenotype is going to dissapear.
Example, I'm working with a species of fish. I'm working woth 6 populations, 3 live in some pools with high density of predators, 3 live in pools with low density. I'm observing some differences in the pheotype. For example, in sites with predation the fishes reach sexual maturity earlier, have bigger broods, with lots more embryos (are livebearers), more broods. Where sites with no predation, have smaller broods.
¿Why? because in the predation sites, the late bloomers are eaten before they have kids. Fishes must mature early and have as much progeny as they can, before they die.
If this fishes keep being in separate pools, some othe differences may appear, until they can no longer interbrees and they'll be differente species.
There are a lot of examples of evolution. Although I know fellow biologist who believe in evolution and in God. You can too... it's all about finding a balance.