I feel I should start by talking about the etymological origins of the words warg and worg.
Warg or worg etymology can be found in the Old English word "wearg" and the Old High German word "warg", which translates to strangler or choker. It is also connected to the Old Norse word "vargr", which means wolf (the plural for wolves is "vargar"). Similar words are also found in other Germanic and Scandinavian languages.
It therefore comes as no surprise that J. R. R. Tolkien, who was very fond of languages and making his own languages, adopted the word warg for his books set in Middle-Earth. The word warg was used to describe the large horse-sized canines ridden by orcs within the stories.
Now that that is out of the way I wish to discuss the topic at hand: The Breeding of Wargs, at least from a fantasy writers' perspective. Or possibly a science fiction writers' perspective. Which is to say, a theoretical sense, and not necessarily meant to be taken seriously.
Part One: Conventional Breeding
Start 
with the biggest wolves and dogs you can find. Feed them. Train them to 
fight. Choose from amongst them the biggest and meanest to breed.
Ideally
 it would be good to start with dire wolves (canis dirus), which were 
about 25% bigger than modern grey wolves (canis lupus), but unless you 
have access to some prehistoric wolves that weigh about 150 pounds well 
then beggars cannot be choosers.
Note - Some dog breeds (Eg. English Mastiffs, Bully Kuttas, etc) can grow to 200 to 300 lbs, making them good examples of dogs that could be used for such breeding. The largest dog ever recorded was a 340 lb English Mastiff. Bully Kuttas is an example of a breed of dog that was specifically bred for war, but also used as guard dogs and hunting dogs. The fundamental difference is that Bully Kuttas were bred over a short period, whereas wargs would need to be bred over a much longer time period.
Next what you need is time. 
Wolves take two years to reach maturity, but often don't breed until 
they are three years old or older. With each successive generation you 
want to be breeding bigger and bigger wolves, while prioritizing their 
viciousness and any traits desirable for breeding them specifically for 
war.
However there are downsides to this gradual increase in size and constant breeding.
#1.
 Inbreeding can result in the resulting 'proto dire wolves' being more 
vulnerable to disease. Possibly including venereal diseases which could 
kill off entire generations of the canines.
#2. The bigger mammals get the longer it will take them to reach sexual maturity.
#3.
 It will take millennia to breed canines that are as big as horses, at 
which point they won't reach sexual maturity until they are 6 or 8 years
 old, which lengthens the amount of time between successive generations.
#4.
 Larger mammal size also leads to generally longer gestation periods. A 
common wolf's gestation period is 62 to 75 days, but something the size 
of a warg would have a gestation period of 11 to 12 months. Thus by the 
time wargs have reached their ideal size, roughly equivalent in size to a
 horse, it would take approximately 7 to 9 years for them to reach 
sexual maturity and produce offspring.
For reference the gestation period of African Elephants is 21 to 22 months, while a mouse has a gestation period of 20 days.
Now
 you might think that wolves or dogs cannot possibly be selectively bred
 into wargs, otherwise they would already exist. Well, dire wolves did 
historically exist, but either died off or bred with smaller wolves, 
resulting in their breed disappearing.
Or perhaps you think that a
 few millennias is too short a time to breed a much larger type of 
canine. But you might be forgetting that horses were only domesticated 
6000 years ago, and were certainly a lot smaller than modern horse 
breeds like Percherons, Shires, Clydesdales and Belgian Drafts. Early 
horses about 6000 years ago only weighed about 800 pounds (about the 
size of an Arabian horse), but some of those larger breeds I just 
mentioned can be about 2200 pounds. So yes, if you breed for size you 
can significantly increase the size of a subspecies in the space of 
thousands of years.
But therein lies the problem of why this has 
never been done. It would take thousands of years to breed wolves into 
something the size of wargs. You would need a culture of people obsessed
 with warfare in order to breed such canines. As per Tolkien's 
Middle-Earth, this makes a bit of sense when it comes to orcs.
Side
 Topic: The word orc is related to the following words: Orc, meaning a 
type of ogre, a variant of which is found in the Old English epic of 
Beowulf. Orcneas, an Old English word that means monsters. The Latin 
word orcus which means hell. The Italian word orcus which means demonic 
monster. Lastly, orca, which is another word for a killer whale.
Part Two: Magical Breeding
Depending
 upon the magic system within the individual fantasy world it should be 
possible to use magic to speed up the process of breeding a larger 
species.
The matter of How is interesting however because the 
wizard, mystic or whatever kind of magic user (mage?) could be using 
many different methods.
#1. Time Travel (Variant 1)
Go 
back in time to find samples of large canines and bring them forward in 
time to conduct breeding, and then return them to the past so that the 
timeline is not disrupted.
#2. Time Travel (Variant 2)
Travel
 forward in time to when wargs already exist and borrow (or steal) a few
 wargs for breeding purposes. This effectively assumes a time loop in 
which wargs would only have ever existed thanks to a time paradox, or an
 alternate timeline in which wargs were conventionally bred.
#3. Transmutation / Alteration Magic
If
 you polymorph a mouse into a warg, can the warg breed with other 
canines to produce offspring? Or what if you transformed a smaller 
canine into a larger canine? Does the magic alter the creature on the 
genetic level? If yes, then it should be possible to use various methods
 to create giant wolves that could be used for breeding wargs.
#4. Illusion
Okay,
 so this is a bit complicated. Depending upon the magic system, it is 
generally accepted that if the person seeing and interacting with the 
illusion believes that it is real then it effectively is real, hence why
 someone could still be killed by an illusionary guillotine. If the 
magic system dictates that illusions are completely fake, and that it 
doesn't matter whether someone believes in them or not, then this isn't 
going to work. If it is the former and the female canine believes the 
male is real, then she should still get pregnant as a result of breeding
 with an illusionary warg.
#5. Shadow or Demi-Shadow Magic
As
 above, but using Shadow Magic, which in some magic systems is 
considered to be partially real and partially illusion, and likewise 
follows the principle that belief influences reality. Thus the shadow 
magic warg can still breed, and was always considered to be at least 
partially real even at the beginning regardless of whether the female 
canine believes or not. Furthermore, this could lead to a breed of wargs
 ("Shadow Wargs") that might possess abilities pertaining to shadow 
magic, possibly useful for stalking their enemies and prey. 
#6. Evolution Magic or Genetic Magic
The
 breeding pairs effectively remain unchanged, but the magic user alters 
the genetics or speeds up the evolutionary process using magic to affect
 the unborn fetuses. Having such magic allows the wizard/etc to "Play 
God" and create many new species. If such magic exists in the fantasy 
world then there should be lots of weird species as a result. Eg. 
Gryphons and unicorns certainly, but also "shark-bears", giant monkeys, 
and miniature elephants that people keep as pets. Thus such magic could be interpreted as belonging in a High Magic setting.
#7. Magical Modification
Skip
 the breeding process entirely and just magically modify canines to suit
 your purpose by transforming and improving them. This could result in 
many different variations of wargs that are the result of 
experimentation.
Part Three: Genetic Experimentation
In 
the Genetìc Experimentation scenario we ignore magic and instead go 
"Full Jurassic Park" using CRISPR or similar technology to modify, 
mutate or speed up the evolutionary process.
How someone could 
theoretically do this can be done in many different ways, especially 
since the author doesn't technically need to adhere to scientific means 
in a realistic sense.
Not much of a scientific explanation is given for why the gamma radiation infused serum can create Hulk Dogs. It is just there as a plot device to give the dogs and the main villain their powers.
In theory a writer can just sort of bodge together a method that doesn't necessarily have to make scientific sense, but I recommend doing the opposite. Come up with a scientific means, as detailed and as realistic as you can make it. It doesn't have to be perfect, but try to make it interesting.
Part Four: Mutation or Natural Evolution
Just because some versions of wargs were selectively bred and designed for warfare doesn't mean that the wargs in your story have to be that way too. You could simply rely upon wargs existing naturally, as the result of evolution. Or perhaps the first warg was simply a mutation and the subspecies is the result of that one warg parenting a lot of children who went on to propogate the breed.
Part Five: Variants and Crossbreeding
Various types of wargs could be bred for:
- Speed
 - Tracking or Hunting
 - Riding
 - Massive Size
 - Thicker Hides
 - Woolly Fur
 - Toughness
 - Swimming
 - Colour (for camouflage purposes) 
 
There
 could also be wargs that are magically/genetically enhanced or modified
 so that they have wings capable of gliding or flying, breathing fire, 
or other abilities.
One of the fastest ways to give wargs unusual
 abilities would be to crossbreed them with unusual canines, such as 
fire-breathing hell hounds in order to create hellish wargs. Or to 
crossbreed the wargs with a magical species capable of breeding with 
many types of creatures, such as dragons. Eg. Half-Dragon Wargs.
Or it could be the result of alien crossbreeding, similar to the Xenomorphs from the Alien franchise.
Of
 course, this may depend upon how silly you want to get with your wargs.
 You might decide your fantasy world doesn't need any hellish wargs with
 dragon wings. Because that's just too silly!
Meanwhile other writers might decide they're writing a comedy and embrace such silliness. 
Speaking for Myself
So how are wargs bred in Korovia/Aoerth? Well, they were bred using dire
 wolves as the starting point over thousands of years, with various magicks used as well to 
enhance their strength and viciousness, and in the case of yarnawolves to enhance their abilities to create a large intelligent wolf which with icy breath. So a combination of factors went
 into making wargs as big as horses in my world, as well as making a variety of other breeds.
As a writer I have embraced a wide spectrum of canines within my storytelling, including:
- Dire Wolves
 - Half Dire Wolves / Mixed Breeds
 - Yarnawolves / Winter Wolves
 - Wargs
 - Half-Wargs
 - Xarsian Wolves (intelligent, having a hive mind)
 - Korovian Wolfhounds (effectively just a breed of white dog, similar in size to a German Shepherd, but resembling a Korean chindokkae dog.)
 
For me I have a great affection for dogs and wolves of all kinds, which is why I find this topic to be of particular interest. But I can also recall a time when I was 5 years old when I was really scared of dogs and wouldn't go near them. Thus I can appreciate what Tolkien and other writers have done by tapping into both mankind's fear of dogs/wolves, but also our love of dogs. I am especially fond of dog stories such as Lassie, various stories by Terhune, The Call of the Wild, Balto, White Fang, etc.
As such various types of canines, both wolves and dogs, have appeared in my fantasy stories. However if you just want a taste of such stories I recommend checking out my short story: "A Hound Named Hunter", which is available in both ebook and paperback.
 




