How it works in the UK, at least for printed books, is that libraries keep records of every loan over the course of a year, and then at the end of each year there's a single national pot of money that's split up among the publishers (and, ultimately, authors) in proportion to the popularity of the books. I only came across this recently: a news story saying that last year's shareout came to 6p per loan, which came as a surprise to me as I'd always kind-of assumed they got nothing.

Peter