First, consider what predictions can be inferred from evolutionary theory. Then test those predictions.
Here's one, off the top of my head.
Prediction: That DNA sequences along an evolutionary path should show progressive amounts of change. Species near each other on the path should have more similar DNA than species further apart.
Find examples where this is not true and you've falsified this prediction.
Duck-billed platipus. Genetically-altered pigs carrying organs for human medical use.