After beating the game and entering the Hall of Fame, you can visit the new area, Ramanas Park, in the southern part of the Sinnoh region—replacing the Pal Park from the original games. Inside, Legendary Pokémon can be encountered and captured, but you must place special slates onto the pedestals inside in order to summon them.
Kanto Slate 
Genome Slate 
Stratospheric Slate
Three such slates, shown above, are the Kanto Slate, the Genome Slate, and the Stratospheric Slate, which resemble Game Boy and Game Boy Advance cartridges.
Some Pokémon that can be found through inserting the slates are exclusive to one specific version—Raikou, Entei, Suicune, and Ho-Oh are exclusive to Brilliant Diamond while Articuno, Zapdos, Moltres, and Lugia are exclusive to Shining Pearl. These may not be the only version differences, too, but were the examples provided ahead of the games’ release.
Where to Find Slates
This information will be made available shortly after the official release of Pokémon Brilliant Diamond and Shining Pearl.
Version Exclusives
Brilliant Diamond
- Raikou
- Entei
- Suicune
- Ho-Oh
- ?????
Shining Pearl
- Articuno
- Zapdos
- Moltres
- Lugia
- ?????
Both Versions
- Mewtwo
- Rayquaza
- ?????