The process is similar to the synthesis of eukaryotic proteins. The Virus high-jacks the cells transcription machinery(RNA Polymerase) to produce Viral RNA. The Viral RNA is then translated to viral proteins using the cells Ribosomes(tRNA).
To be brief where every you see human DNA in the protein synthesis step, replace it with Viral DNA. Whenever you see human RNA in the protein synthesis step replace it with Viral RNA.
Exceptions exist of course but this is a straightforward rubric to get anyone started.
