All dogs are descendants of wolves, but the "breeding" was done unknowingly by primitive peoples. Packs of wolves would follow nomadic tribes who hunted animals. Out of any pack of wolves there's always going to be a more social, less aggressive one that will catch the attention of these primitive hunters, such that the hunter will toss a scrap of leftover meat to the friendlier wolf.
Because the friendlier wolves got more meat scraps, or to put another way, were more favored by the ancient humans, they were more likely to survive, and hence, pass on their "more friendly genes."
Over time, a miniature form of evolution began occurring, in which wolves began evolving into what we now know as dogs, because the friendlier, less aggressive wolves were cared for by the hunters, while the aggressive meaner wolves went without scraps of meat and had to hunt themselves, and wolves have only a 20% kill rate.
The friendlier wolves proliferated, and also, it was a win-win because these wolves hung around and followed the nomads, and acted as watchmen, howling and yapping to alert them of any danger like an approaching cougar, etc.
Over time the canines' appearance began changing, and the environment they were in (being "cared for" by the nomads) favored or selected for socialness. Every so often in nature a gene mutation occurs. If in this setting, the mutation was an even MORE friendlier gene, then that gene was passed onto offspring, further ensuring the evolution of dogs from wolves.
So why, then, did dogs end up looking so different from wolves? Because genes that are associated with more social behaviors also just happened to come with components that caused altered appearance. Not too long ago a researcher tested this theory with foxes. He bred a bunch of foxes and separated the aggressive ones from the people-friendly ones. He kept breeding only the people-friendly ones, and would continue breeding only the most people-friendly from each litter. After many years, having created a much more social fox, there were also changes in appearance such as curlier tails or fur, changes in fur color, and other subtle changes, but not enough that it was a different species.
Thank you all for letting me info dump!