You can apply for the free case through Apple's web site starting late next week. The company plans to source cases from third parties due to a shortage in bumper cases, so iPhone 4 customers will have a choice of a few different cases. If you are still not satisfied with the iPhone, you can return it for a full refund within 30 days of your purchase. Steve Jobs said plainly about the decision that "we want to make everyone happy, and if we can't make you happy we'll give you a full refund."
The move comes three weeks and a day after the first customers began taking their new iPhones home and experiencing both antenna and proximity sensor issues. The growing backlash against Apple escalated earlier this week after Consumer Reports said they would not recommend the device, even though it comes in at the top of their smartphone ratings. This was followed by rumors of a possible recall, posts being pulled down from the Apple forums and finally today's conference.
Edit (2:25 p.m. ET): Jobs acknowledged that the case offer will be international.