The Dream World is a new aspect of the games, shown as part of a website called the Pokémon Global Link. The Dream World is accessed by sending your Pokémon using the Game Sync option of the C Gear. From here, you use the Dream Smoke obtained by Musharna and sync your game up to your Pokémon Global Link account located on the official site; http://www.pokemon-gl.com
So you send the Pokemon you want to Pokemon DW and then play the minigames. After that you will go to a tree and you will be able to bring back any of the Pokemon You played with to the Entralink. Once that is done just go use the C-Gear and use the Entralink to get your Pokemon. There are lots of videos of it on Youtube.