Do Dogs Come from Wolves?
The exact origin of today’s dog is unclear, but studies show both dogs and wolves evolved from an extinct species of wolf of European origin that lived 30,000 years ago. So domesticated dogs came from wolves, but domesticated dogs did not evolve from the modern gray wolf we see today.
How did Dogs Evolve From Wolves?
Researchers have shown that while the modern day gray wolf is related to dogs genetically, dogs are not direct descendants of the modern gray wolf. According to studies, the gray wolf and dog separated from a common ancestor at least 27,000 years ago (so 30,000 is a rough estimate). That common ancestor wolf, called a Taimyr, is since extinct.
To sum this up, dogs and gray wolves come from the same common ancestor, a type of now-extinct wolf called a Taimyr that lived nearly 30,000 years ago. Below we explore the details of the early divergence of the domestic dog, its ancestors, and admixture into high-latitude breeds.
TIP: Check out some studies on the evolution of the domesticated dog yourself: Ancient Wolf Genome Reveals an Early Divergence of Domestic Dog Ancestors and Admixture into High-Latitude Breeds, Complete Mitochondrial Genomes of Ancient Canids Suggest a European Origin of Domestic Dogs, and Genome Sequencing Highlights the Dynamic Early History of Dogs.
How Were Wolves Domesticated?
During the time of the Ice Age, due to limited resources, wolves had to look for alternative resources for food. Historians assume the domestication process started when wolves adapted to lingering around humans for their scrapped food, this slowly allowed one another to get close to each other, without fighting or fleeing. Studies also suggest that just like humans with their babies, gazing into the eyes of a dog releases oxytocin which creates a social connection between the two. With the humans brain and tools, plus the wolves extraordinary senses and hunting skill together they could hunt larger and more game. 
From Domesticated Wolves to Dogs
When you have a small population of domesticated wolves together, they continually interbreed which causes mutations in genes. These can be minor things such as pointed ears, fluffy tail, or different colored eyes, etc. A bigger mutation could include being the runt of the litter. Normally, survival of the fittest might kill off the runt, but with human intervention. The runt would survive and breed more frequently. Dogs of all different shapes, sizes and features can result because of this. Research also suggests that breeding an animal based solely on their ability to be tamed (tame-ability) could naturally alter genes to become more sociable to humans (as demonstrated in the fox to dog experiment). 
Fox to Dog Experiment
Researchers selected silver foxes to be domesticated and bred them for their tame-ability to see if genes would naturally change to benefit human interaction. In doing so, the researchers found that in only a few generations, the foxes were showing similar patterns in behavior, physiologically and morphologically to domesticated dogs. Some of the foxes by the sixth generation were whining and wagging their tails for human attention much like a dog would. The study suggests that the domestication of any animal will result in genetic changes allowing the animal to be more sociable to humans. 
What is a Canid?
Canid is the term used to describe animals that share similar genes with dogs such as coyotes, wolves, and foxes. They all have genetic similarities, suggesting a common ancestor. Domesticated Dogs are also a part of this family but show to have intermixed with wolves continually, while other canids usually mated within their gene pool. Canids typically travel in pairs or packs and are carnivores, but are resourceful and don’t mind eating plants for extra energy as they are long distance hunters. 
NOTE: The Canis Lepophagus is a canid that existed during the Pleistocene era about 2.5 million years ago in North America and could be the base ancestor between wolves and coyotes.