First off, just in case you weren't aware, you need wifi to access Dream World.
Secondly, you need your DS system (not just your Pokemon game) connected to wifi. When you first turn on your DS, go past the warning message and click Systems (the little spanner next to your White card). You will need to set up internet connection in that part first.
Also note that if you're using a R4 card or something similar, wifi might not work out (it didn't work for me).