Technology Research News has an occasional series entitled "How It Works," describing in relatively straightforward language how important technological or scientific processes are accomplished. The latest is on "self-assembly," with a focus on biological replication. Self-assembly is particularly important for working at the nanoscale, as top-down assembly tools are simply too big and unwieldy to build anything quickly. Such techniques can mimic or even use DNA as a base for replication.

I think the TRN piece doesn't go quite far enough in explaining how the DNA and protein tools are used, but it's a good start for understanding the basic processes involved.