Previously, the DNA analysis of the genome of prehistoric wolves and dogs support the idea of a two-step domestication process. The first one was the evolution of wolves through a mutually beneficial relationship with humans, sharing food and space.
The second one was the active breeding of dogs by humans in order to select dogs which were adapted to the current needs (hunting, tracking, pet).
Furthermore, there are two main hypotheses to explain the first domestication step (http://www.americanscientist.org/issues/pub/early-canid-domestication-the-farm-fox-experiment):
1) “Self-domestication” by the wolves: Some wolves lived in the vicinity of the camps of the nomadic hunter-gatherers to eat the garbage left by the prehistoric people. Those that were less anxious thrived and continued to follow the humans, generation after generation, and gradually the first dogs emerged from this group.
2) The prehistoric people actively selected wolf pups and let only the most docile ones reproduce. After several generations, the first dogs emerged. This hypothesis has been being tested in Novosibirsk since 1959, where foxes are being bred for “tamability.”