Hey, don't use your card right away when you do expire. Check the archives. Some guys just posted a deal that gets 2? 3? months for a buck or something like that.
Quick, off top of my head, run down. Anywhere between immediately or up to a week after expiration your Xbox homepage should offer a deal to re-up Live at the idiotically cheap price.
Think the dude said a full year, if it works out, ends up being like $12.
It was a pretty recent topic so should be easy to find.
Here, found it: http://slickdeals.net/f/6009880-Xbox-Live-Gold-2-months-for-2-weblink
Looks like you have to make sure auto-renew is turned off for the weblink to work.