First off, a warning:
Pokemon transferred from GBA games to Diamond and Pearl CAN NOT be transferred back. Make 100% sure you want to transfer the pokemon before bringing it into Pal Park!
Now, make sure you have your GBA Pokemon game in Slot 2 (put it in before turning the system on, of course). You'll notice a menu option called "transfer." By using this option, you'll be able to bring 6 of your GBA pokes into Pal Park.
When you enter Pal Park, you'll be able to play a new minigame where you must find and catch your pokemon. They will be in either the tall grass or the water, depending on what type of pokemon they are. When you find one, use a poke ball on it and it will be added to your Diamond/Pearl roster. While you can leave the park at any time, you can't transfer over any more pokemon until you catch the six you originally brought in. You can also only upload 6 pokemon a day.
The pokemon you bring in retain all their stats and abilities from the previous game, including trainer name, ID, and held items. So not only can you bring your old buddies into Sinnoh, but you can re-use your old valuables, as well!