First make sure the pokemon you want to migrate are in PC boxes in emerald. You cannot migrate pokemon with HMs so visit the Move Deleter to delete those moves if the pokemon know them.
Put the game in the GBA slot of your DS. Then in Diamond you need to beat the Elite Four and gain the National Dex.
Go to the end of Route 221 (south of Sandgem Town) to open up the Pal Park.
Save and restart, choose "Migrate from Emerald" in the first menu. You then choose the 6 pokemon you want to migrate.
Then in Diamond, go into Pal Park and do a "catching show". Make sure you take a pokemon that knows Surf, because some pokemon you will only get on the water.