You will need 2 DSs. Put one of each game in each DS, and (in both) go to the top of any Pokemon Centre. Talk to the woman in the middle to go into the Union room, and then talk to the player from your other game. Select a trade, and then ... do the trade =P
There is no way to transfer Pokemon over, so you will need Pokemon you don't want on Platinum to trade over to your other game. Good luck!