Legendary Dogs

Just go in between routes until one face "disappears". This means that it is on the same route as you.
Suggestions:
1. Save once the Pokemon is on the same route as you.
2. Have a good amount of ultra balls.
3. Have a Pokemon that knows block or mean look with you.
4. If you get frustrated, just press and hold A+B just as the
ball hits the pokemon. If you time it just right, this
will catch the Pokemon in one shot. This is the only "legit" cathing trick with out cheating. (AR)

Entei and Raikou are randomly running around Johto. You must be lucky to run into them. In order to locate where they are at, check the Pokegear's map. I'd suggest using a Max Repel if you end up in the same route at them.

You have to use the same "Route-to-Route" strategy as Diamond/Pearl/Platinum. Basically, find two adjacent routes (i.e. Routes 38 & 39) and walk to the border of the two routes. When you find the border, cross over it continuously. As you cross the "Border", open your Pokegear and check the map. As you continue to cross the border, the legendary Pokemon in question will work their way through the region. Have patience; it may take some time before they're on the same route as you. Once you know for certain you have them on the same route as you, just walk into any patch of grass along that route. Also, all of the roaming Pokemon will try to run before the battle begins, so any Pokemon that knows "Mean Look" (Gastly, Haunter, or Sableye) or has the ability "Arena Trap" (Trapinch or Diglett), will be of great benefit. Also to note if you're trying to catch the legendary "cats" (not "dogs"), Entei & Raikou, they know the move "Roar", so you'll have to start all over if that happens. Last, but not least, any damage you manage to inflict on any roaming Pokemon will remain, even the ammount of PP for their moves will get depleted to 0 if you encounter them a lot. Hope I've help in any way and happy hunting!