Okay, Ninja Monkey basically summed it up for you, but if you're wondering any specific teqniques to encounter it, and how to get it, then listen up:
What you will need:
Level 49 Wobbufet or a level 49 pokemon that can induce sleep with great speed, also holding quick claw, or both, except with Wobbuffet at a higher level than 52 or so.
As much max, super, or normal repels as you can hold.
A pokemon that can fly.
What to do with them:
When you first beat the elite four, one of the three will roam around Kanto's various routes. Start at any route you choose, then use a repel of any type, then move the direction of the character without taking any steps, that way the repels will remain in effect as long as you do that. Now with repel, it blocks all pokemon encounters in the wild EXCEPT for those pokemon whose level is higher than your lead pokemon's level. And when you get lucky enough to encounter it, if you have a level 49 Wobbuffet in front, you can use mirror coat against a thunderbolt, ember, etc., but thats riskier because the legendary dogs have roar, so you could have that level 49 pokemon that can induce sleep(or freeze them) to do its magic;however, if they're not fast enough, the dogs will flee. But if it can work its magic, inflict a good bit of damage so that its in semi-low orange health(not farther than that; if you kill it, then you have to turn your game off and repeat the processes all over again, unless you saved before this), then swap out for a Wobbuffet above level 50. and constantly try to capture him, and if he wakes up, with Wobbuffet's Shadow Tag ability, he can't immediately escape, unless he uses roar as soon as it wakes up( by now you mustve noticed that I have given the dogs a gender; i assume its an entei and i assume it male because of the third movie). If you get it, hooray, if not, the process will be that much easier because you now know its location due to the pokedex. This is where fly comes in. Usually, when you attempt to fly to its location, it will immediately swap to a new one as soon as you take one step into that area(you can take a step back and forth from the boundaries of each area to see that effect; however it doesn't always work) so try either flying to the same city repeatedly to get it in an area nearer you, or if you're at a route with a building you can keep going in and out to swap its area until its in your routes area, and then repeat the catching processes that I explained earlier. Of course, you can cheat to make it more efficient to obtain it, but that would've wasted all this hard work that I took in typing this, for I typed this by memory, not by any guide or other internet site.
