What is Pal Park?
Pal Park is where Generation III ends and Generation IV begins. In Diamond and Pearl it sits at the end of Route 221, south across the water from Sandgem Town, run by Professor Oak, and it opens once you hold the National Pokédex. In HeartGold and SoulSilver the same institution takes over Fuchsia City's old Safari Zone grounds in Kanto. Either way, the rule of the place is absolute: Pokémon come in, and they never go back.
The crossing starts at the title screen. With a Ruby, Sapphire, Emerald, FireRed or LeafGreen cartridge in the DS's Game Boy Advance slot, and the Advance game in the same language as the DS game, a migrate option appears. Choose exactly six Pokémon, none of them knowing an HM move, confirm, and they are gone from the Advance save forever, waiting for you inside the park.
Inside, migration becomes a sport called the Catching Show. You are handed six Park Balls, which never fail, and sent into the park's field, forest, mountain, pond and sea areas to find your own six Pokémon again in the habitats matching their natures. The show is scored on your time and the variety of what you catch, and pays out in berries.
Sinnoh's park rationed the traffic: one migration of six per Advance cartridge per 24 hours, and fiddling with the DS clock only extended the wait. HeartGold and SoulSilver dropped the daily limit entirely. Because the whole system hangs on the Game Boy Advance slot, it needs an original DS or DS Lite; a DSi or 3DS cannot migrate at all.