Instructions
Go to a Pokemon Center. Pokemon Centers are red-roofed buildings with a Pokeball emblem above the door located in most major towns and cities. Enter the center through the front door and walk to the PC boxes on the main floor.
Face the PC box and press "A" to access your Pokemon storage vault. If you want to delete a Pokemon that is a member of your current party, select the "Deposit" option and select a Pokemon from your party using the D-pad. Press "A" to deposit the selected Pokemon in storage.
Use your D-pad to select the "Release" option from the PC Box menu and press "A." Use your D-pad to select a Pokemon in your PC box. Press "A" again to delete the Pokemon from your PC box. Press "B" to exit your PC box and save your game. The deleted Pokemon will no longer appear in your party or in your PC box.