This offer is only for those with a Kindle Fire with Special Offers (KFSO):$2 Credit on Apps and Games in the Amazon Appstore
From the home page of your KFSO, swipe the top menu to the left until you see Offers, then press/click in order to see the current offers. Click on the offer, then on the orange button to add the credit directly to your account. It's nearly instant and the next screen offers to take you to Amazon so you can spend that credit away! If you miss that screen, though, don't worry - a document about the offer will appear on your home page.
You can shop from your Kindle Fire or your PC, but you need to check for any individual product that is excluded from this (and all other) promotions, on the product detail page and I don't know if you can see that info on the mobile pages you get on the Fire itself. You must sign up by Midnight January 1, 2013 and use the credit by midnight, Jan 8.
You might as well apply this one to your account right away, since it will apply automatically to any eligible purchase.
This deal drops the cost of premium games such as Angry Birds Star Wars Premium HD or PAC-MAN HD down to 99 cents or is enough pick up a one or two of games such as Skylanders Cloud Patrol or Pudding Monsters HD, at no charge. Always check the compatibility before buying, to make sure it will run on the device you intend to use and don't assume anything from the name (that last one has HD in the name, but works on every device I have, including my phone; others I've seen with HD in the name won't work at all on the Kindle Fire HD devices). To make your credit go the furthest, check out some of the sale games on the New Releases or Bestseller pages, such as Monopoly MILLIONAIRE and Need for Speed Most Wanted for only 99 cents, marked down from $5 and $7! If you are searching for something more educational, for your little ones, Team Umizoomi Math: Zoom into Numbers and several other Nickelodeon games are also 99 cents or less right now.
