Sadly, yes you do need wifi.
You must first have good wireless(wi-fi) internet. Then you must get on the Global Link site and set up a account. After setting up a account you must collect the dream smoke in the game from the Sleeping pokemon. It should be holding the item. After that the main menu should have another bar. Press a on that bar and sync it with your game (most likely through Friend Code) And enter the Dream world. On the website you can find the pokemon, Grow berries which you can't do in the game, and find pokemon with irregular abilities.