If you've already encountered them, then this advice will be usefull. Otherwise, randomly walk around, and if you're religious, pray.
Step 1 - Preparation
>> Train a Paras/Parasect until it learns spore, but keep it under lvl 40. Give it quick claw and totally jack up its speed using carbos. Have pokemon than know: a paralyzing move and disable, mean look or spider web, a confusing attack, a good accuracy reducing move, and fly. Lots of regular pokeballs as well as ultra balls. Fast balls, contrary to popular belief, do not work.
Step 2 - The hunt
>> Buy lots and lots and lots of max repels. Fly to New Bark. Check your pokedex for the legendary dogs nest. If it says Route 29, you're in luck. Otherwise just keep on flying to New Bark. Once the dog is currently at Route 29, put on a max repel and walk into the grass. A cleanse tag also helps, as well as sweet scent or playing pokemon march on the radio, although these dont make it incredibally easier. It's still mainly luck. Walk around until you a) encounter the dog, go to step 3, or b) the max repel wears off. If it wears off, first check your pokedex to see if the dog is still in the area. If yes, use another max repel and keep walking. If no, start from the beginning of this step.
Step 3 - Trapping the Legend
>> Paras(ect) should be the first member. Use spore. Hope you go first. If not, your screwed and have to start back at step 2. If the dog is sleepened, hit it with meanlook/spider web and then a confusing attack. Then reduce it's accuracy as much as possible. Paralyze the dog. It will immediately not be asleep and try to use roar. Hope that the parlysis, confusion, and accuracy reducing makes the attack not work. Without switching pokemon, use disable to disable roar. The dog can no longer use roar, and it cannot simply run away (because of the mean look/spider web). If it does manage to get away earlier in this step (before the disable) then start back at step 2. Note: it will retain its status. So if it ran away under paralysis, the next time you see it, it will still be paralyzed.
Step 4 - Captured
>> Now that it can't run, the rest should be easy. Use attacks and wear it down. When its health turns orange, use very weak attacks, unless its still confused. You don't want to kill the dog or for the dog to kill itself because of confusion. Once it is very weak, reput it to sleep. Then start chucking balls like crazy. If you use a regular pokeball press UP + B when you throw it and release UP when the ball opens up. It is rumored that this increases the effectiveness to beyond that of an ultra ball. Personally, I use this strategy but since it is unproven, you could always throw regualr ultra balls.
My Dog Pound Team:
Paras - Spore
Raichu - Thunder wave
Alakazam - Disable (i actually need to switch after thunder waving, but zammy is really fast)
Gengar - Confuse ray, mean look
Magmar - smokescreen
raticate - super fang, tackle