One way in which you confirm a theory... Prediction...

A couple of generalizations
According to evolution, you should find more primitive life forms the farther back in time you go; and that's exactly what we see.
According to evolution, you should see random mutations in DNA; and that's exactly what we see.

A couple of specifics
Darwin predicted that precursors to the trilobite would be found in pre-Silurian rocks. He was correct: they were subsequently found.

Very specifically - The recent find of the Tiktaalik fossil. Scientists looked at evolutionary theory, the fossil record, and determined:

If we go to this section of Greenland(place), dig down to this level (date), we should find a creature with XYZ features... After 10 years of searching, they found almost exactly what they were looking for, exactly in the geologic layer they said they would find it, and it has most of the physiological features they predicted they would find. It was just luck, and a bonus that they ended up finding one of the most complete fossils in paleontologist history.