The same way you test anything in science. You make predictions based on the theory and test them. Think of it as a series of "if/then" statements. "If this aspect of evolutionary theory is correct, then we should see this under these conditions."

An example of this that has been used to test one aspect of past evolution is:
If this group of animals is more closely related to each other than to other animals, then we should see that their DNA sequences are more similar to each other than to other animals (based on what we know about how DNA is passed down with modification).

And indeed, that is what we see.