How does bibliomancy work?
It uses a book as a divination tool
Bibliomancy is one of a number of ways of divination (which is along the same lines as Tarot cards, numerology, astrology, and the like).
The person concentrates on the question involved, or simply asks for guidance, and then randomly flips through the book they are using (often the Bible, but it can be any book) to arrive at a certain page and whatever passage the eye alights upon on that page, that is the answer.
So that is the How To Do behind bibliomancy. As to the How Does It Work... I'll answer it this way - the answers that someone seeks is oftentimes already known and the passage that comes up merely triggers what is already known and brings it to light. (Note - I believe there is more to this than that, but this explanation is a decent first pass answer).