This offer is for those with the Kindle Wi-Fi with Special Offers only. Turn on your wireless, click Menu, Sync & Check for New Items, then on View Special Offers after the sync has completed. You should see a new offer:
$10 for a $20 Amazon.com Gift Card
Click on offer, then click on the link to get an email with the offer, which expires on May 4.
You'll get an email with a link to the special $10 for a $20 Amazon.com Gift Card page. Don't one-click, but use the Add to Cart button. Then click on Proceed to Checkout, sign in and then enter the promotion code you received via email (mine was practically instantaneous) where it says Gift Cards & Promotional Codes and click on Apply. Double check your Order total and place the order. You'll get a gift card via next day delivery (I'd prefer it in email and you have to think it would have been cheaper for Amazon and/or the sponsoring advertiser, but who am I to turn down what is essentially a half-price offer on any order up to $20?). I'll let you know when I get it tomorrow if it looks like it will work on Agency titles in the Kindle store (most gift cards do and the offer B&N had like this worked on nookbooks).