Question

how do we come to know that organisms have a common ancestor?

Answer 1

When you look at proteins primary structure we can see there are a lot of conserved residues when you look at closely related species. As you compare more and more organisms you can eventually see that many of the residues are conserved to a such degree that they most come from a common ancestor.

You can use the method above for DNA as well and it support the theory about a common ancestor.