You cannot get a blank DS cartridge. There are manafactured for Nintendo by a company named Macronix. They use Mask ROMs, which means the game is programmed into the cartridge during the manafacturing of the cartridge, so it can't be overwritten.
They are numerous flash carts for the GBA and DS that can often hold a memory card. ROM files are put onto the memory card and can be played back on the DS.
Popular ones are R4 and Acekard.
http://en.wikipedia.org/wiki/Nintendo_DS_storage_devices
cartridge
Route 228 (after you get the National Pokedex, insert a Pokemon Leafgreen cartridge into the Nintendo DS's GBA cartridge slot)
the cartridge
Route 208, Route 210 (After obtaining the National Pokedex, insert Sapphire cartridge into your DS).
The game ID for a Nintendo DS game can be found on the cartridge. There will be a code, which is specific for each DS game.
cartridge
The DS doesn't have a digital store, all the games for regular DS and the DS lite are either on GBA cartridge, or DS cartridge.
Route 228 (after you get the National Pokedex, insert a Pokemon Leafgreen cartridge into the Nintendo DS's GBA cartridge slot)
the cartridge
Game Boy Advance game cartridge. They can be played on the DS by placing them in the GBA cartridge slot in the bottom of the DS.
In a DS you should be able to play GBA games in the slot that is underneath the DS. There is a cartridge slot for DS games and a cartridge slot for GBA games. This is the same with DS lite as well.
The data is saved onto the cartridge. Remember that the DS and DS lite do not have internal memory.
A GBA cartridge is a:Game Boy Advance cartridge.
Insert the Pokémon Emerald cartridge into the Nintendo DS and you can find it in Route 216, 217 and Lake Arcuity.
Route 208, Route 210 (After obtaining the National Pokedex, insert Sapphire cartridge into your DS).
You can put a GBA cartridge into the Slot-2 of an original DS, or DS lite.
upgrade it then