The viral genome directs the host cell's metabolic machinery (ribosomes, tRNA, nutrients, energy, enzymes, etc.) to synthesize viral enzymes and viral parts. The viral genome is transcribed into viral mRNA that goes to the host cell's ribosomes where it is translated into viral structural proteins and viral enzymes. During the early phase of replication, the viral genome replicates thousands of times. During the late phase of replication, viral structural proteins (capsid and matrix proteins, envelope glycoproteins, etc.) and the enzymes involved in maturation are produced. Also during this time, envelope glycoproteins coded by the viral genome of enveloped viruses are incorporated into the host cell's membranes.
In the case of most RNA viruses, replication and assembly occurs in the host cell's cytoplasm. With DNA viruses, the viral genome enters the nucleus of the host cell and here is transcribed into viral mRNA. The viral mRNA molecules then leave the nucleus through the pores in the nuclear membrane and are translated into viral proteins by the host cell's ribosomes in the cytoplasm. Most of these viral proteins then re-enter the nucleus where the virus assembles around the replicated genomes.