There are several different trainer cards you can unlock in Pokemon Black for the DS. Here is the list of cards you can unlock, and how to unlock them.
Black Card – Complete the National Pokedex
Gold Card – Find all Pokemon Musical Items
Green Card – You start the game with this card
Purple Card – Beat the Elite Four
Red Card – Get a Forty-Nine streak in both Super Single and Super Double Subway lines in the Battle Subway
Silver Card – Unlock all Entralink Powers