This discourse is basically a logical bridge between an old school religion and a new school religion. First, the philosophers debate the existence of God, and they find that even for all their skepticism and reservation, they cannot see an existence such as the existence of their reality without concluding some force outside that reality which might be called "God." However, the skepticism with which they treat that first premise is the tone of the book, and one might say that in the end, they have invented "science."
Natural religion is exactly what they are attempting by cautiously and curiously entertaining ideas. If the mark of old school religion is belief and superstition, then these three philosophers seem to demonstrate the exact opposite of that. Instead of lofty ideas, they stay close to skepticism, often dismantling ideas with the entire force of their intellect, which of course is secretly Hume's own intellect. Therefore, the book traces out what religion means to a highly skeptical person.
In the end, the process of religion becomes a discourse on logic and reason, where the thinkers agree that the risks of concluding incorrectly and then carrying false beliefs are serious enough to be scientifically avoided at all costs. This commitment to proof and the suspension of belief lead to a treatment of reality that seems not religious at all. In fact, the three philosophers begin to accuse one another of hyper-skepticism or superstitious belief. Basically, Hume is on team skepticism. His book can be seen as a prophecy for a new age of philosophy. The reader who likes Hume's point of view will likely also appreciate Ayer and the Logical Positivists.