DNA unzips prior to cell reproduction, and it begins when the enzyme gyrase puts a nick into one end of the double helix strand. Another enzyme, helicase, slowly unwinds the strand as proteins form to keep the sides separated. More enzymes add nucleotides, check the pairing and form new strands.
The DNA doesn't all unzip at once. As the gyrase starts to unzip that one end, it separates the rungs on the DNA ladder, one base pair at a time. As the double helix separates, DNA polymerase starts adding the correct nucleotides on each strand, while a subset of that enzyme makes sure the pairs are in the correct sequence.
Ligase starts to seal up the newly formed pairs into a new strand of DNA. Once the old DNA strand has been completely unzipped and the two new strands built, each new strand automatically winds into the helix shape.
At one point in the replication process, one end of the original double helix DNA strand, the two separated portions containing only half of the nucleotides and the two assembled strands are all still connected. The part where the two new strands are connected to the parent strand is called the replication fork, which moves down the strand as the process continues.