So the evidence is that since we have a similar body plan the DNA is similar.
A little more to it than that.
There's the fossil record, which shows a gradual transition over time.
There are atavisms and signs of vestigiality with primates, such as occurances of humans with semi-functional tails, the grasp reflex that certain infants are born with (chimp babies have this in order to grasp onto their mothers fur...human babies do tis, despite the fact human mothers have nothing for a baby to grasp onto, and it disappears after a few weeks), and the presence of things like goosebumps. These and other examples are predictions of evolution and lend support to it.
There are ERVs, which crossconfirm phylogeny and shows that we share about a dozen ERVs with chimps. The odds of a single ERV randomly popping into the same place between two unrelated organisms is about 1 in 3 billion. We 'just so happen' to share about a dozen of them. Process that.
There's the fused on chromosome 2, which was predicted as a result of evolution. All the other great apes possess 24 pairs of chromosomes...humans only have 23. If evolution is correct, the common ancestor to great apes would have to have 23 pairs or 24 pairs. If the former is correct, then the ancestors to the great ape must have had one of their chromosomes divide into two pairs. If the latter is true, then the ancestors unique to humans should have a fused chromosome - two that became one. And guess what we found? A fused chromosome. Exactly what we expected to find. Were scientists just lucky? Did they just make a really good guess? I mean, really, what are the odds that
the exact thing they expected to find would be there, staring them in the face?
But yeah - aside from all that stuff - and other things I'm leaving out - it's just similarities.