There are many people trying to learn more details about this subject and the reason is that the domestication of the wolf is one of the most important events in human history. Due to this, man gained the opportunity to stop nomadic life and start farming and stockraising little by little.
Initially, as mentioned above, today's wolf and the dog we know come from a generation of wolves that has been extinct for thousands of years under the name Canis cf. Lupus. This ancestor was bigger and stronger than today's wolves. The prevailing view is that these beasts saw the benefits of following humans and eating from their leftovers instead of hunting. So they approached people, got acquainted with them and stopped being afraid and shy of them. Man then saw the benefits of having these incredible beasts near him either as protection or as support in hunting. Over the years, through human genetic selection (choosing the friendliest and best animals to keep and discarding the rest), these wild animals acquired traits such as communication skills with humans by better understanding our signals. Eventually they came to live harmoniously with us and to become our best friends.
There are various theories about where and when the wolf was domesticated and there is a theory that claims that it did not happen only once and in one place, but twice. The site is likely to be southern China, Mongolia, or Europe, and the prevailing theory as to when claims that it occurred more than 20,000 years ago. In all paleontological matters there is still great uncertainty considering that the only evidence we have is the fossils we find, resulting in that we are still unable to determine beyond reasonable doubt many things. However, it is an issue that, as said earlier, is of great interest to many people and we will definitely have more updated information soon!