I am going to go a strictly biological route.
TL;DR: It's all hormones.
The lunar cycle is strongly (superstitiously?) reminiscent of the menstrual cycle.
This is confirmed with a quick google search. It is a bit interesting that in humans, the menstrual cycle and the lunar cycle are (on average) exactly the same length. Clicking on a few of the most popular links (and as says on wikipedia), they have no correlation to the modern human. However, I found at least one study saying there is at least a correlation, if no definite causation. Which means we have an at-least-plausible example of very strong hormone change/cycle being caused by the moon.
A lesser example is simple circadian rhythms. Although to be called "circadian" they have to last about a day (24 hours), there are other rhythms that last different amounts of time. Circadian rhythms are most strongly associated with periods of light vs darkness (especially natural light, from the sun).
So we, as humans, are already at least slightly influenced by the movements of our celestial neighbors. Obviously the association with the moon is very, very faint so as to be indistinguishable in modern times, and the association with the sun is easily negated by artificial light, but the influences are there.
I always imagined werewolves to have similar influences, but for them to be a lot stronger. Instead of, say, ovulating and bleeding at a certain time of month, the werewolf's celestially-dictated hormones cause the lycanthropic change. If you want this only to happen at night, you could also have the hormones connect with the sun as well as the moon, circadian-like.
How would the infection happen? Assuming we are going for a werewolf's bite causes the wounded to become a werewolf, I think the simplest would be a virus. The virus infects the host's hormone-producing organs to produce the hormones necessary for lycanthropy, and off we go. If the infection can only happen during the shape change, it's simple to only have the virus present in the saliva when the hormones dictate the change.
This would also give the potential for a cure (or at least a treatment). After all, if all it is is hormones, birth control is a very simple form of hormone therapy, and it has radical influences on menstruation.