While we have a fair bit of overlap, given that this predates written history, you may want to consider X-posting this to /r/AskAnthropology as well as this falls within their purview. And for that matter, I would note that /r/AskScience would also be an appropriate venue given the biological science aspects of the question.

I am no expert on the matter nor do I have a comprehensive answer but I may send you in the right direction in finding a satisfying explanation.

I’ve read the book Honden zoals ze echt zijn ( Dogs, how they really are – sorry, its only in Dutch available) by Chris Dusauchoit.

FYI: C. Dusauchoit is a Belgian Journalist specialized in televisions shows on animals. He’s not a biologist, anthropologist or anything alike. Anyway, in one of the chapters he writes about the domestication of wolves and mentions two theories on how this may have happened:

The first one paints a rather romantic image in which an in bearskin dressed caveman stole a little pup from its mothers nest and raised it into an obedient pet. This theory has been refuted since pupnapping isn’t as easy as it may sound. First, To obtain a tame wolf you have to take the pup from its mother and the pack on the twelfth day since it has been born. On this day it opens its eyes and ears, and starts to recognize the pack members and its environment. Stealing a pup in Neolithic times is not only a precarious endeavor but requires the cavemen to know when the pup was born...

If the pupnapping was successful, there is only one week to imprint on the animal or any prospects on banding with the animal will be lost. Secondly, a twelve day old pup needs milk to survive. Breastfeeding a wolf seems implausible.

Thirdly, if you want a pack of domesticated wolves you have to find a male wolf who is willing to breed with your bitch on heat, which only happens once in two years. According to this theory, domesticating wolves by stealing pups is possible but highly unlikely for prescientific times. I don’t have Dusauchoit’s book by the hand so I can’t give you any references or further readings, sorry.

A secondary theory was presented by Raymond and Lorna Coppinger, behavorial ecologist and sled dog racers. They state that wolves were attracted by offal near man’s settlements. The less shy wolves came the closest which led to contact and eventually domestication.

This may give you an idea on how domestication of wolves took place but I suggest you read one of their books; Dogs: A New Understanding of Canine Origin, Behavior and Evolution or What is a dog? to find an exhaustive answer.