Since viruses are not actually living things (because they do not grow, do not have homeostasis, and do not metabolize) I don't think they produce like anything else (neither sexually nor asexually).
They reproduce by first infecting a living cell. They rely on host cells to reproduce because they lack the enzymes necessary for metabolism and have no structures to make protein. Then, the bacterial virus (bacteriophage) punches a hole in the cell wall and injects its DNA into the cell. Or, a plant virus enters a plant cell through tiny rips in the cell wall at points of injury. Animal viruses enter host cells through endocytosis. Then, viruses either go through the lytic or lysogenic cycle.
In the lytic cycle, the virus attaches to a cell and injects it own bacterial DNA. Then the viral genes control the host cell and force it to replicate viral genes and to make viral proteins, such as caspids. The proteins are then combined with new copies of DNA, to make new complete viruses. Then, the host cell breaks open and releases the new viruses.
During the lysogenic cycle, the viral DNA is replicated and embedded into the bacterial DNA so it copies, but doesn't destroy the host cell. Symptoms may not appear for a long time. Then, something triggers the virus and it goes through the lytic cycle.
Most of this information (some of it word for word) came from my Biology textbook, "Biology: Principles and Explorations" by Holt, Rinehart, and Winston.
Hope that was clear enough and that it helps!
Lytic cycle and lysogenic cycle
The difference is that in lytic cycle, the virus kills the cell immediately.
The genetic material of a virus enters a living host cell and takes over the translational and transcriptional mechanisms of the cell in order to replicate the virus's nucleic acids
the Lytic Cycle
Viral reproduction. See more in the related questions below.
Replication of self using materials and energy of the invaded living cell ("reproduction"), along with viral mutations.
Over- nourished . Viruses depend on a healthy cell for reproduction.
The maturation stage
the viral reproduction is a virus that can't be stoped
May provide reproductions events on a squence
the Lytic Cycle
Viral reproduction. See more in the related questions below.
Replication of self using materials and energy of the invaded living cell ("reproduction"), along with viral mutations.
destruction of cells by viral reproduction .
The maturation stage
Over- nourished . Viruses depend on a healthy cell for reproduction.
destruction of cells by viral reproduction
destruction of cells by viral reproduction
destruction of cells by viral reproduction
It occurs in a cell that's been overtaken by a virus.