To catch Deoxys in Pokemon SoulSilver Version, players must transfer Deoxys to Pal Park from Ruby, Sapphire or Emerald Version. The only way to get Deoxys into Pal Park is to use an existing saved game and transfer the Pokemon into Pal Park using the GameBoy Advance slot on the Nintendo DS.
To catch Deoxys in HeartGold or SoulSilver Version, players must first have captured Deoxys in Ruby, Sapphire or Emerald Version. The GameBoy Advance game cart with the saved game on it should be inserted it into the GBA slot on a Nintendo DS or DSLite. The HeartGold or SoulSilver version should then be inserted into the DS cart slot and the game should be started.
According to Bulbapedia, the only way to capture Deoxys is to encounter him in Pal Park. Pal Park itself can only be reached with use of HM03 (Surf). Even after players reach Pal Park, they will not be able to enter until they have filled out the entire Sinnoh Pokedex and have obtained the National Pokedex.
Once the National Pokedex is in possession, players must head to the park and speak with Professor Oak on Route 221. The "Migrate From" option should be selected on the main menu screen, and there will then be an opportunity to choose Pokemon to import from the GameBoy Advance game. Once Deoxys is selected, it will be released into the wild.
After releasing Deoxys into Pal Park, players simply have to wander the area until they encounter it. Capturing it is a simple process, as the special Park Ball has a 100 percent catch rate.
It is important to note that once Deoxys is transferred out of the GameBoy Advance game, it will no longer be accessible on that cart.