How does one demonstrate knowing how to program during an interview process if one doesn't know at least a fair amount about the language and its basic methodology?
Candidate should be able to answer any questions in pseudo code. You are right that each language has its own intricacies, and e.g. perfect code in C is terrible code in C++, but C++ is not specific enough that general programming principles don't apply.
Reading a book about the language over the weekend before the interview won't make an experienced programmer out of you, but you will know what the language is about and you will have a good overview of most features of the language.
Besides, in my experience at least, candidates who have a lot of experience in the language that's used don't gain as many points as the ones who know ins and outs and best practices for libraries and frameworks which are used in the organization.