Players cannot catch Kyogre in-game in Pokémon Soul Silver. However, players can transfer him by way of Pal Park from a number of other Pokémon games.
In Pokémon Heart Gold, players can find Kyogre in the Embedded Tower, which is accessible from a cave in Route 47 if players have the Blue Orb. When players reach that same point in Soul Silver with the Red Orb in their possession, they find Groudon waiting for them instead.
Players can only obtain Kyogre in Soul Silver by trading for him, or by importing him from another game. Kyogre is available from the Cave of Origin in Pokémon Sapphire, or the Marine Cave in Pokémon Emerald. Since these games were only available for the Game Boy Advance, however, they require a model of Nintendo DS that has the appropriate cartridge slot. Players who have a DSi or 3DS model will not be able to obtain Kyogre this way and must trade for him or use a copy of Heart Gold.
Kyogre is a legendary Pokémon, and in all games starts out at level 50. Players will need to be at a fairly high level to win the battle, and should come prepared for strong ice and water attacks.