This question doesn't concern how it might be possible for a human to take on werewolf form. I'm asking about what impact the lunar cycle has on a human body and any other possible ideas of what might cause a werewolf to shift, not how a process of shifting might actually work.
Hope that makes sense!
I don't see a science tag on this question, so I will go supernatural on this.
The moon acts as a mirror for sunlight, effectively reflecting some of the sun's light back to Earth, during our night, making it a little less dark.
Those sun rays that are bounced off the moon have some of their characteristics changed - they are now charged with Moon mana or something - and irradiate living beings differently. Werewolves and other lycanthropes' skins are more sensitive to this magical radiation, and past a certain level they will shapeshift. The threshold is reached and passed naturally during the full moon.
A mad enough witch or wizard could maybe force such transformation by emulating moonlight in some way.
See also Blutz Waves, under Conditions for Transformation, for how they approached this in the Dragon Ball series.
The way that disease works, I see 2 good, realistic options;
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.
Post-answer thoughts
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.
In IMDb's description of Werewolf of London, a movie from 1938, it says...
While in Tibet looking for a specimen of the Mariphasa lupina lumina, an obscure phosphorescent plant that only grows in the mountains of Tibet and blooms in moonlight, botanist Dr Wilfred Glendon (Henry Hull) is attacked by some kind of animal...
What if it wasn't the animal attack which made Dr. Glendon a werewolf? What if it was caused by the flower's pollen, which only comes out in full moonlight? It is therefore not the moon which calls the wolf; it is the moon which calls the flower which calls the wolf.
It's the UV light and, thereby, the feeding cycle.
The light of the moon is reflected sunlight. This light extends into the ultraviolet spectrum, which most humans can't see into, but canines can. And what does this allow them to do? To more-easily see and track prey, relying on signs that don't show in the regular spectrum:
"There are many examples of things that reflect UV, which UV sensitive animals could see that humans can't," co-author Ronald Douglas told Discovery News. "Examples are patterns on flowers that indicate where nectar is, urine trails that lead to prey, and reindeer could see polar bears as snow reflects UV, but white fur does not."
A reindeer, a cat and a dog could therefore probably see a white-furred animal, such as a bunny, hopping through a snow blizzard, while most people would just see a blur of all white.
Therefore a werewolf's best meals will come by the light of the full moon -- and on that night a werewolf could be satiated for a month. (It'll still eat in human form, for both biological and social reasons. But the big, glorious feast comes once a month.)
A werewolf could turn at other times, but it's not worth it -- turning takes a lot out of the werewolf physically; he needs a few days to recover enough to do it again. To one who can see into the UV spectrum, though, the full moon really lights up the night sky. (Source: personal experience.) So a werewolf will restrain himself as the moon waxes full, holding it until the right night, and then go for it.
The moon doesn't turn werewolves; the moon is the cue.
Just like the moon pulls up tides, it pulls out the wolf hiding inside the human.
All humans have it a bit, as can be seen in high rates of insomnia and first-aid emergencies during the nights around the full moon. When the moon grows, something wakes in your blood. It wakes and must come out.
Just like tides vary from almost non-existent like the closed-in Mediterranean to the pace of a galloping horse on the coast of Normandy the top of the range comes out as full-blooded lycanthropy.
The full moon makes it lighter at night.
Humans were once preyed on by large cats. Cats can see better in the dark than we can, but they cannot see in total darkness, nor well by mere starlight. Ditto wolves.
So we may be wired to be more alert, more jumpy, less able to sleep soundly, when the moon is full. And wolves may be wired to go hunting. There's a grain of truth to the belief that mental patients become more disturbed under a full moon.
Easy to deny primeval instincts and reflexes, but they are still there. Why do we get hiccups? Apparently the neural pathway is something that was very important for a fish. The vestiges persist.
Maybe in a werewolf the human and dog reactions to the lunar cycle synergize?
I'm going to go with legal issues on this one. In werewolf society for reasons that might seem archaic to the latest generation, it is illegal to transform except during a full moon. Physically, any werewolf can transform at any time, but the fines, red-tape, and social ostracism that come with breaking from tradition ensure that the majority of well-behaved werewolves will only activate their transformation during a full moon.
Having studied how the moon might impact humans, I think I can give you some insights.
Taking from a biological perspective, the moon does indeed affect animals: http://www.livescience.com/37928-ways-the-moon-affects-animals.html
From this, some creatures set particular biological processes, such as the coral reef's reproduction, on the full moon.
Furthermore, the moon has a weak magnetic field: https://en.wikipedia.org/wiki/Magnetic_field_of_the_Moon
And the moon is impacted by the earth's magnetotail when it is behind the earth (which has the best odds of also being a full moon, facing the sun): https://www.sciencedaily.com/releases/2008/04/080420123319.htm
My own personal theory is the moon affects magnetite found in the human brain: https://en.wikipedia.org/wiki/Magnetite
Magnetite in the human brain: https://www.ncbi.nlm.nih.gov/pubmed/1502184
So from this, we could speculate that the moon affects a particular biological process, in that, in distorting or interacting with earth's magnetotail it has a knock on effect on the magnetic field of earth, causing the magnetite in the human brain to effectively change, which in theory triggers things like headaches.
From a fiction perspective, you can then argue that such a change causes people to become angry, or mad (it's where we get the word 'lunatic' from: lunar), which causes them to become werewolf-esque in behaviour.
In terms of physical changes, it'd be harder to justify, and you'd have to suspend any sort of hard sci-fi approach here. You could argue the magnetic field causes the DNA to transform (mostly affecting the exposed outer skin), which starts a few days before the full moon and slowly disappears a few days after.
But you could go hard sci-fi and have the person act like a werewolf. Their rage triggering adrenaline would enhance their strength, which again, superhuman strength isn't unheard of: https://en.wikipedia.org/wiki/Superhuman_strength
But obviously a physical transformation would be a step too far in a hard sci-fi. You could make it that the DNA or genes (perhaps modified by a retrovirus or even parasite?) makes the person noticeably hairier and stronger, but it would assume a permanent fixture rather than an instantaneous change.
I've seen the idea used in such stories that it is the polarized light that does it.
Dependence on the moon is lightly tossed aside with a comment that the necessary components of moonlight (specific frequencies of polarized light) have been isolated, and his Polaroid "Were-flash" lets him turn into a wolf or back to his human form at any time, its controls having been designed to be operable even with paws and no opposable thumbs.
However, with any idea that it's something about the moonlight, why is it specific to the full moon, and not just any bright moon? The full moon is brightest compared to other times of the month, but how bright that is depends on atmospheric conditions.
