My first university biology classes begin in September. In preparation, but increasingly out of curiosity, I've been studying some basic biology. Saying that to say, I know as much about DNA replication as the Khan Academy videos teach.
Presently, I'm reading about the two efforts to sequence the genome. From what I've read, Collins' project used "polymerase catalysis and nucleotide labeling"; whereas, Venter's project used "shotgun sequencing". I didn't know enough to understand the article I read on "shotgun sequencing" and couldn't find one that described the other technique.
I suspect that, in order to comprehend a concise description of the two techniques, I'd need to learn more than I could learn from an answer to this question. That said, it'd still be nice to have a very rough idea of what each process involves and how they differ from each other. A crude analogy to something concrete would be great.