On closer examination the operations are so complicated that the non-chemist is tempted to suspect it can't really happen. It happens anyway. The non-chemist shrugs, but wonders how such a complicated way of doing business arose. It must have come about through evolution. The mistakes are called mutations.
Sexual reproduction brings changes too, by reshuffling the genes of the parents.
Many of these changes make little difference. Once in a while, though, the novelty turns out to be an advantage. That all depends on the environment of the day. If circumstances are right the novelty will catch on. To ask about the evolution of DNA is to ask about the evolution of evolution itself.