Firstly, you need a Nintendo DS or DS Lite. DSi or 3DS will not work as they do not have a GBA cartridge slot. You also need a 4th or 5th gen game for the Nintendo DS, i.e Diamond, Pearl, Platinum, Heart Gold, Soulsilver, Black/White or their sequels. You may need to pass some sort of requirement to migrate Pokemon to the newer games, in Diamond/Pearl you need to have beaten the Elite Four. I am not sure about other games as I have not played them. If you have fulfilled a requirement, turn on the Nintendo DS with both the DS Game and GBA Pak inserted. Run the DS game. When you get to the menu it should have Your Save, New Game Wifi settings and migrate Pokemon from Sapphire, which you click. It will warn you that your Pokemon cannot be returned to the gameboy, then select 6 Pokemon you wish to send to your DS game. You can only migrate once every 24 hours, and if you change the time on your DS the game will sync itself to that and reset the 24hr timer.
Once you have migrated your Pokemon, in my experience with D/P there is a location in game you must go to 'catch' your migrated Pokemon, in Sinnoh it is called the Pal Park. The pokemon are instantly caught in this artificial environment. When you catch them from Pal park they will be in a habitat that suits them, Celebi in the grass, water pokemon in the lake etc.
I hope this helps you migrate your Pokemon:) Also, I don't know if there will be compatibility issues with a Japanese GBA cartridge. Message me if you have questions or concerns Meteor :)