"Proof" of evolution...
Evolution is a theory, like most of the explanations in the sciences that deal with the past, it is likely to remain a theory (at least without detailed records from a civilization that exists for a few hundreds of millenia), however there is a body of evidence to suggest that it occurs, which has been drawn from direct observations.
Firstly, random mutations causing changes to an organism. In the negative side this could be cancer, or some genetic condition turning up in a person with no family history of that condition.
Secondly, natural selection. This can be seen in many instances, either by the slower of the gazelles being caught by the faster of the cheetahs, or by the oft-quoted example of the peppered moth (which I will not repeat here to save space. Various genetic experiments have proven beyond most doubt that characteristics can be passed on through generations, so it stands to reason that if a trait causes members of a species to survive, then it is more likely to be kept.
Some mutations will have both good and bad factors (such as the one that causes sickle cell anemia, which can provide a resistance to malaria), and therefore the trait will be more likely to be kept under certain stresses (i.e. an area with a high chance of catching malaria) and lost under others.
The simplest example of both these factors in action is in viruses, where mutations to the genes that code for the coating of a virus can make it undetectable by the immune system even if there is a resistance to the virus before the mutation.
While this does not prove that evolution did occur, it shows the mechanisms by which it might occur, and suggests ways for species to become separated (e.g. different beneficial mutations arising in separate populations of the same species).