I'm assuming that you have registered etc and are already in the Dream World. You just need to go across the rainbow bridge to the "Island of Dreams."
As you go through the forest you will sometimes see bushes rustling. Click them and a Pokemon will appear. Play the mini-game to befriend them.
After going through 10 areas you get to the "Tree of Dreams" where you can pick one of the Pokemon you befriended to take back to the Entralink.
After exiting the Dream World, warp to the Entralink in your copy of Black/White. Go north into the forest and you will see the Pokemon there. Go into battle and you will find a Dream Ball in your bag - use that, it has 100% capture rate.
Although I did catch a Shinx in a Premier Ball instead. But you don't get to keep the Dream Ball if you didn't use it :(