How Do You Catch The Legendary Dogs In Soul Silver?

Use your Poke gear map. You'll only be able to find Raikou and Entei this way. Don't fly to them otherwise they'll run somewhere else. And also get a Pokemon that knows Block or Mean Look, so they won't run away. Trust me, they'll run.

After you initially encounter the dogs in Burned Tower in Ecruteak, the dogs flee into the wild as you approach them, initiating the hunt. Entei and Raikou will continue to roam the entire Johto region throughout the game and can be randomely encountered in the wild like any other pokemon, until you either catch, or defeat them. You can view their current positions in the game by looking at your PokeGear map. Their positions change constantly, as you move from route to route, so the best approach to take concerning them is to travel between two routes swiftly and let them eventually come to you. Monitoring their positions on the Pokegear while you do this, when they finally come to a route adjacent to you, surf or walk through grass in that EXACT same region and they will apear, just as any random wild pokemon would.  It is imperative that the pokemon you use to encounter the two wild dogs has an ability that will hinder the dogs' abilities to flee, such as sandtrap or shadow tag (I used Wobbaffet), lest either of them would flee after the 1st turn.

Suicune however, does not roam the wild freely. Rather, you encounter Suicune several times in the game as a stationary pokemon, but it flees the first four times. After you encounter it for the second time in Kanto, you can battle with Suicune, north of Cerulean after you have earned the Cascade Badge (Misty's Gym).

They run to a different location every time you move into a new route. The trick is to move back and forth between 2 routes and check your pokegear each time. They will inevitably land in your route and then you go and look in the grass for them.. Cathing them is a different matter. Status changers ftw..

Just like vulcanfury said the dogs roam around every where becase really suicune does count. He roams till eventuly he lets you get to him.

@other guest (who said you don't)

drugs are BAD, my friend. Did no one warn you?

You know, they're actually cats... But yeah. Pokegear map all the way. I actually just caught Entei.