In order to migrate from Emerald, or any of the Gen III games, your Nintendo DS system must have a GBA Cartridge slot, meaning yes, you must have either a DS Lite or a regular DS. The DSi, DSi XL, and 3DS do not have the slot to play GBA games.
If you do have a DS Lite or DS, then you must first insert your Emerald version into the GBA Slot of your system. Then, go to the Main Menu of your DPPt game, and choose "Migrate from Emerald." Choose the 6 pokemon, then go back to the main menu, and play the game. Once you are in the DPPt game, proceed to go to the end of Route 221, where you will find Pal Park. In there, you may catch all the pokemon you have chosen to migrate.