When you try to change the store (ie, the country) associated with your AppleID, you are told that:
"You need a valid method of payment and a billing address for a country or region in which iTunes is available."
It's been a while, so I don't remember exactly how it's done. That being said...
I'm fairly certain that you have to create a new Apple ID in order to do this (you cannot have more than 1 country on the same Apple ID). You create a new one by changing the country of the iTunes store page (the small flag icon at the bottom-right of most pagesdon't create an account yet). Unless they've changed it, I believe you can make a new account without payment info by attempting to download a free app (which triggers the "login or register now" but doesn't ask for payment info) but you cannot download anything other than free content until you put a form of payment in (of course). Either way, you should be able to use an iTunes gift card purchased from the country of origin to get around needing a credit card from that country.
Again, my memory is a bit hazy so the details may be a bit different or things may have changed since then, but this is more/less how it's done.