The short answer is that they don’t.
So why has this become so popular in our culture? Why do wolves howl at the moon in books and movies? Why do werewolves get all wolf-y at the full moon? That’s a good question because even those who have researched this question are still confused.
Wolves howling at the moon appears in the mythology and stories of many cultures. Most of our current perceptions are from Native American culture, with a smattering of Greek. For example, the Seneca tribe believes that a wolf sang the moon into existence. In Greek mythos one of the goddesses of the moon, Hecate is associated with a pack of dogs that travels with her. Diana, the Roman version of Artemis, and sometimes the goddess of the moon, inherited the dogs as well. Norse mythology says that night and day are summoned by a pair of wolves, one of whom chases the sun, and the other chases the moon.
But where all of these stories came from is unclear. It may have something to do with increased frequency of wolves being spotted on the full moon, but that likely has to do with the increased light rather than any special affinity for the moon itself. This is just another one of those stories that show up between different cultures that, as far as we know, had not met prior to European expansionism.
Wolves have a very eerie howl and sometimes it sounds like distorted human singing. But instead of howling at the moon, wolves are generally howling to each other. They use howls to contact each other, to warn others off, and sometimes just as a little cheerful cry to let those around them know they’re awake.
So wolves aren’t really howling at the moon because they one day hope to return to it. They’re just particularly big puppers who want to be able to find their friends.