In most stories, werewolves transform in the full moon. However, Nirn has two moons, so that changes things. Lore-wise, when does a werewolf transform? Also, how do the moon cycles work in Nirn?

Werewolves transform every night in the Elder Scrolls, except for the strain the Companions have which allows them to transform at will once per day. The moons don't really work like anything that could exist in reality because of the way the space around them is twisted, so you end with both moons being in different phases most of the time.

If you scroll down you can find all of the phases of the moons http://www.uesp.net/wiki/Lore:Khajiit.

So with Bloodmoon werewolves, would you transform every single night whether you like it or not? I could have sworn I read somewhere it was more of an occasional thing.

I'm not entirely sure about the player, but NCPs at least apparently transform every night.