You keep the card in your wallet. You already protect that very well, and even if it does get stolen the thief is none the wiser since there are many tens of thousands of possible password combinations on the card. Choosing strong passwords and writing them down is recommended by the likes of security guru Bruce Schneier and Microsoft security expert Jesper Johanson.
You can use the PasswordCard on its own, but it also combines excellently with password storage tools such as KeePass. You can use the PasswordCard to generate the passwords, so that you can use the card itself as paper backup for when you don't have access to your password storage tool, and you can use PasswordCard to generate and remember your master password.