Being a natural nitpicker, I'll start off with some of the problems in this scenario.
You have left out a few important details about dragons - specifically their size and life/reproductive cycles. Let's say that a dragon grows to 1000 lbs, stays with its parents for the first 20 years of life, then takes a mate at age twenty, and has a reproductive span of 30 years - in other words, more or less like humans.
First, dragons must have just arrived on the scene, so the obvious question is: where have they been hiding themselves?
And why must they be recent? Because up until (roughly) the 20th century, homo sapiens would have been easy meat for draco sapiens. The rise of technological civilization would have been close to impossible, since cities would have been nothing more than snack bars for the lizards. Worse, they'd have devastated the planet. Starting with a single 20-year-old pair of dragons, in the absence of disease or intraspecies conflict, the population grows like this:
Year 1 - 2 dragons.
Year 10 - 32 dragons (30 young)
Year 20 - 62 dragons (60 young)
Year 30 - 332 dragons (300 young)
Year 40 - 1025 dragons (963 young)
Year 50 - 3587 dragons (3255 young)
Year 100 - 2 million dragons (1.8 million young)
Year 150 - 1 billion dragons (998 million young)
You can see where this is going. So let's say that young dragons, being typically immature, kill their siblings so that only half of any brood survive, although the first generation have a 100% survival rate. Then the adult population looks like
Year 1 - 2 adults
Year 10 - 2 adults
Year 20 - 2 adults
Year 30 - 32 adults
Year 40 - 62 adults
Year 50 - 195 adults
Year 60 - 529 adults
Year 70 - 1,391 adults
Year 80 - 4,011 adults
Year 90 - 10,552 adults
Year 100 - 29,488 adults
Year 150 - 4.5 million adults
Year 200 - 689 million adults and so it goes.
Notice that http://www.livescience.com/23310-serengeti.html gives the total population of the Serengeti plains at 750,000 zebra (call it 800 lbs apiece), 1.2 million wildebeest (500 lbs apiece) and "several hundred thousand" others (let's say 500,000 at 300 lbs apiece, although many are smaller). That's total of 1.35 billion pounds of prey. At 1000 pounds per day, this herd will feed 3700 dragons for one year. This means that within 100 years the dragon population will have scoured the earth clean of anything big enough to catch and eat.
So there will have to be some mechanism in place to cut down on the reproductive success of the dragons. Limiting clutches to 3 young every 10 years seems a good start, but it only delays the problem.
So, how in the world are people going to domesticate dragons? The above numbers, oddly enough, provide a possibility. With the prolonged draconian childhood, it's clear that adults must have a strong protective instinct toward their young. This suggests that perhaps humans, by some quirk of reptilian psychology, trigger the same indulgent/protective instincts as the young, similar to the way infants of other species produce attachment in humans. Since dragons aren't very bright (by human standards), people could take advantage of the dragons' instincts. This would allow people to survive around dragons long enough to select out those individuals which can be tamed, and eventually produce a domesticable breeding line. At the same time, people could also begin a quiet program of population control to keep the dragon numbers to a bearable level. It would also be important to monitor the dragon population for the appearance of individuals who don't like people, and quietly dispose of them.
Of course, this ignores the other side of dragon nature. Although adults treat humans as young dragons, presumably young dragons do so as well - and young dragons kill their own. And at any given time, about 90% of the population is young. Frankly, I'm a bit short of ideas on how to deal with this.
And to honest, I'm not at all sure how these convenient draco deaths will be eventuated. That is left as an exercise to the reader.
Other than military uses, it seems unlikely that anybody other than the military could afford one as a pet. Each dragon needs 180 tons of meat per year. And, given the metabolic peculiarities of such a beast, I'd expect the poop to be toxic and corrosive. A few might be used for very high-status races, or perhaps as high-speed couriers, but the expenses for any other use would be prohibitive.