It should just be the month and year that the card was issued to you. Some cards have it on them, some don't. It's usually right next to the expiration date...for instance, I've had a couple cards in the past that would say something like this:

Valid: 05/04-05/06, or something along those lines. In that case, the "start" date would be 05-2004.

Your best bet might be to call the seller and ask them what they want you to put down. If they aren't used to dealing with international sales, then they should call the credit card company themselves and ask them what they should do in this case (don't let them put all the work on you....you're the customer after all, and they should be able to call their credit card processing company with questions like this anyway.)