The PCR process involves several key steps: denaturation, annealing, and extension. During denaturation, the double-stranded DNA is heated to separate it into two single strands. In the annealing step, short DNA sequences known as primers bind to each strand at specific locations. Finally, in the extension step, a DNA polymerase enzyme synthesizes new strands of DNA by adding nucleotides to the primers. These steps are repeated multiple times to exponentially amplify the target DNA.