So imagine what ToE is saying about DNA: every living thing on the planet uses the same material to reproduce: DNA, aka genes. If this is true, the same core DNA has been replicated and passed on in every organism on the planet. Wow. That's why it's a huge risky prediction to say that all life on earth will be based on DNA. So far, every one has. When they discover new worms living at the heat vents hundreds of feet under the sea, or new bacteria in Antarctica: DNA. ToE predicted that. Thousands of thousands of predictions, and every one borne out.
Further, once it was discovered, DNA gives us a way to confirm many other predictions about the relationships between organisms. The idea is that species change when mutations arise in the DNA ("genome"). So the more mutations, the further apart those two species are related.
Think of what I was saying earlier about homologies. ToE says we will find homologies between species that are closely related. We can look at them to see if they look related, but the differences in their DNA will tell us how close or far apart. Remember the bird and bat wing vs. the bat wing and whale flipper and mole foot? ToE says that the weird homology between the bat wing, mole foot and whale flipper means they are more closely related than the bird and the bat, even though the bird and the bat superficially look alike. And, sure enough, the DNA shows fewer differences between the three mammals than the bird and the mammals.
And remember what I was saying about nested hierarchy? That means that species branch out and develop some, bringing their genetic heritage with them. So, since the bat, mole and whale are all mammals, they will all be warm-blooded, all give birth to live young, all nurse their young--despite their vastly different ways of life.
Another example would be insects. Because they all evolved from a common ancestor, all insects have 3 body parts, no arterial system, 6 legs, lay eggs. Insects are the only invertebrate to evolve flight. Therefore, if you find and invertebrate that flies, you also know that it will have 3 body parts and 6 legs. You just won't find a flying invertebrate with 4 or 8 legs. ToE explains why--exactly why. As Dobzhansky says, nothing in Biology makes sense without evolution.