- Observation of a phenomenon.
- Initial hypothesis explaining the phenomenon.
- Making a testable prediction from the hypothesis.
- Falsification test.
- If it fails, the hypothesis has been disproven. If it succeeds, it has been evidenced.
- Repeat 3-5; the hypothesis becomes a theory, and, eventually, an established scientific fact.
How does evolution do this? Well, let's take an example.
- The initial phenomenon could be as specific as "all mammals have fur" or as general as "biological diversity exists".
- The initial hypothesis is "there existed a species from which all mammals are descended, and evolution by natural selection is the mechanism by which the plethora of mammalian species exist today".
- The testable hypothesis can be anything from predicting further anatomical homology, genetic evidence (e.g., human chromosome #2 being a fusion of two separate chromosomes found in other Great Apes, complete with extra centromeres and telomeres), fossil mammals showing both the same features and common ancestry between two groups of mammals (e.g., Ida), vestigial features (e.g., the recurrent laryngeal nerve, or the vas deferens), etc.
But let's say the prediction is that speciation occurs. After all, if it doesn't, the theory of common descent doesn't work.
- The falsification test is, basically, any attempt to show that speciation occurs. And, lo and behold, it does. We see species split into several independent species naturally in the wild (e.g., all extant lemurs exist on Madagascar), accidentally in human habitat (e.g., nylon-eating bacteria), and artificially in the lab (e.g., fruit flies, E. coli). This aren't just hypothetical past events, these are actual, observable effects.
The evidence for the evolution of all extant species from a single common ancestor is staggering. It really is. It was a valid hypothesis at Darwin's time, quickly became a respected scientific theory, and has since become a scientific fact. It's still a theory of course, but its truth is as undisputed in the scientific community as the existence of atoms: the evidence is so strong that the very nature of reality as we understand it would have to be overturned for evolution to be disproven.
Basically, the theory of common descent is a valid, testable explanation for vast swathes of data and observations, and is supported by an unparalleled variety and plethora of evidence from virtually every field of scientific endeavour.