According to Katherine C. Grier's Pets In America (2006), a company named Spratt's produced the first dry dog food in the 1860s (see page 16). It really took a long time for most consumers to purchase dog food for their dogs--and rightly so. Often this dog food was not very robust ingredient-wise. Moreover, people were simply use to feeding their dogs kitchen/table scraps or getting cuts of low quality meat from their butcher.
There were also different types of dog food. The first types were cake-like and had to be broken apart and softened with water before dogs could eat it. By the 1910s, some companies began selling kibble (287). Canned dog food first appeared in the 1910s as well, though it didn't really become profitable until 1940s (285).
I would highly recommend checking out the rest of Grier's book. She explores the history of pet keeping more generally. Moreover, there are plenty of details I've glossed over, such as common appeals to consumers as to why they should switch over to dog food rather than simply keep feeding them table scraps.
The historian John Cummins has this absolutely fascinating book that might be of interest to you. In The Art of Medieval Hunting: The Hound and the Hawk (1988) he talks extensively about how aristocrats in Europe in the 12-15th centuries took care of their dogs, which were 'working' animals in the respect that their primary function was to hunt. We have lots of interesting documents from the period which are essentially manuals about how one should run a kennel.
One such manual, called The Master of Game, was written by the granduncle of King Edward IV of England -- Edward of Langley, the 2nd Duke of York. In this, he says that one should actually feed dogs on bread most of the time, and that the dogs should only be given meat at the end of a successful hunt. It seems that he had a basic understanding of how behavioural conditioning worked!
He also recommended mixing chopped-up bread with blood and unusable offal from the hunted animal, and, in a sense, 'serving' it to the dogs in the hollowed out carcass of the animal they had killed -- again, to reinforce a positive association in the minds of the dogs. Successful hunt = tasty food. This was called the 'curée' (see p. 41 of The Hound and the Hawk). As you probably guessed from that last word, this, along with many other refined hunting techniques, derived from French courtly practices (many of which are described in Gaston Phoebus' Livre de Chasse, another medieval hunting manual.)
I hope that was interesting and helpful!