The partnership of dog and humans has included assistance with herding and hunting, an early alarm system, and a source of food in addition to the companionship many of us today know and love. But when this partnership happened is at the moment under some controversy.
Recent mitochondrial DNA studies suggest that wolves and dogs split into different species around 100,000 years ago; but whether humans had anything to do with that, no one really knows. Another recent study suggests that the entire population of dogs today are descended from three females near China about 15,000 years ago. The earliest domesticated dog found in China is at the early Neolithic (7000-5800 BC) Jiahu site in Henan Province. European Mesolithic sites like Skateholm (5250-3700 BC) in Sweden have dog burials, proving the value of the furry beasts. A site in Idaho called Jaguar Cave was said to have included dogs some 10,000 years ago, but this site has been redated to no earlier than 4500 bp.
Under normal conditions, I would set a date for the probable domestication of an animal on the conservative side: the date at which the first rock-solid genetic changes were made in an animal. But, if I were a betting woman, I'd say that of all the animals in the world humans have domesticated, the dog would most likely have been the first. So, I'm going to stick my neck out and use the 13,000 year BC date as the probable date of domestication. You (or your teachers) may feel otherwise.