On the opening screen (Where you see the Dialga/Palkia or giratina, hold at the same time
(B+UP+R), After that a blue screen shall appear, Confirming that you want to delete your save file.
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You can't delete a game, as they are on the game cards. If you mean the data, you should be able to delete it in the options menu of that specific game.
lolz
The only time any GBA or DS game ever does that is if the cartridge (game pack) itself is damaged.
At the screen were it shows a picture of Pokemon with all of the options, there should be an option were it says "delete saved data". Press it , and it will ask if you're sure. Click YES! Voila!
You can't.