Through the process of the "Lytic Cycle" of viral reproduction, in most cases by splitting open the cell to release the newly created replicants of the virus. See the related questions below for more...
A virus can: 1. Kill the host cell 2. Alter the cell; incorporate into the genetic material of the host cell, thus becoming part of its nucleic acid pool; or divide when the host cell divides.
A virally infected host cells' "desire" would be to create copies of the virus (as that is what the virus does to its host cell - turn its own mechanisms against itself). The host cell, once...