Naturally I can’t find my copy of Medieval Dogs. I hope some insight from the later medieval Arab world will pique your interest!
Islamic law considers dogs unclean animals, but that did not stop medieval Muslims from keeping dogs as watchdogs, for hunting or, we have some hints, as companion animals. In some cases, Christians were employed as dog handlers, but that was by no means a universal practice.
Muhammad Ibn Mankali's 14th century hunting manual, whose title Housni Shehada wonderfully translates as Merrymaking Among Wild Animals of the Desert, gives us some rare insight into the relationship of people and their dogs. Mankali notes that some hunters disgracefully allow their dogs to sleep with them in their beds and sit on their furniture, and asks God to forgive them this sin. When temperatures dropped, Mankali tells us that Muslims would cover their dogs in clothing. He says this is okay as long as they use rags instead of good fabric. And in what is probably insight into Muslims' relationship with dogs, he urges his readers not to be like those uncivilized Arabs of the desert who sleep with their dogs in their arms.
Shehada found a brief reference in late 15th/early 16th century text that dogs popular among elite women were trained to perform tricks, although there is no further detail. Mankali also mentions a breed of dog "not suitable for hunting" that was favored by performers at markets to take part in puppet shows.
Various manuals that the best way to feed dogs in the winter is once a day, at sunset. In the summer, they should receive small meals throughout the day. The food should be warm, not hot, and it should be meat--meat in meat soup; bones stewed in soup until disintegration. Lentils and dates were prescribed as well, which would have supplied what modern dog owners know to be vitamins and the all-important fiber. Some writers had ideas of ways to enhance mother’s milk for puppies to help them grow faster and stronger.
The manuals are explicit in instructing dog-handlers to pet their dogs! They say stroking, combing, and scritch-scratching dogs with one's own hands on a daily basis is necessary for dogs' health and hunting suitability. The fact that this is written down is actually really interesting. It simultaneously justifies this practice of handling an "unclean" animal that (we understand today) is very helpful to build the kind of relationship that a human-oriented workdog needs, and suggests that such a justification may have been necessary for Muslim dog-handlers. We likewise find instructions to teach puppies that humans are okay by letting them lick honey and oil off dog-handlers’ hands.
I love that the hunting manuals say dogs should sleep near their owners because it will make the dogs smell better. I don't know about that, but I do know that dog ownership gets one used to the smell of dog, dog breath, wet dog, and of course to the incomparable taste of dog hair-flavored mashed potatoes.
There is some attention to caring for pregnant dogs and new puppies as well. Pregant dogs must be allowed to rest rather than hunt, and a special, soft space should be set aside for them at delivery time. (Mother dogs about to deliver indeed "nest".)
As far as training goes, we have the most information concerning hunting dogs. It's important to remember that hunting and veterinary manuals are prescriptive rather than, generally, descriptive sources, but they do give us insight into what types of things were thought suitable. Manuals suggest close attention to astrology when choosing the time of breeding.
Training started with dog selection. That implied first of all close attention to breeding. Saluki-type dogs were thought best for hunting, although apparently some dog-handlers thought a first-generation hybrid of two purebreds would produce the optimal dog. Texts prescribe various ways of selecting the best puppies from a litter, from weight to mother's preference--but explicitly not color.
Positive reinforcement and negative reinforcement positive punishment methods were both used (rewarding successes and punishing failures). Mankali describes a series of steps to progress dogs from puppies licking honey off human hands to full-blown hunters. Again, it is impossible to say how widespread this was in practice, but it offers a useful reference point at least.
At two months, puppies should be induced to follow and find smelly treats like sheepskin and foxtail. At five months, they were to face down fiercesome predators like mice. More formal training began at seven months. The dog-handler would take them into the desert in packs of three to four, one of whom should be an older and experienced dog. There they would hunt an escalating challenging series of prey: jerboas, rabbits, and finally foxes. Often, dogs were training alongside the birds (especially falcons) who would be their eventual formal hunting allies.
As an additional question - these days, there are many breeds of dog available. In, say, medieval England, would there have been many different breeds used for different jobs? I've only really heard mastiffs referenced.