Varicella zoster's replication cycle is categorized as a lysogenic. This is different from a lytic in that it takes longer from the initial infection/exposure for signs and ssymptoms to develop. This period is known as the incubation period and can vary in length depending on the virus. For varicella zoster the incubation period is generally about two weeks.
During these two weeks copies of the viral DNA is made. Initially the virus injects its DNA into the host cell and its DNA integrates with the host's DNA. The cell does not know it is infected and continues with its functions which usually includes mitosis. When the cell makes copies of its own DNA, it unknowingly is also making copies of the viral DNA. During the incubation period numerous new cells containing the viral DNA are created. At the end of the incubation period, the viral DNA is triggered and uses the host cell to start building viruses (this now constitutes the lytic cycle).The cells will rupture and release the viruses.