This offer is only for those with a Kindle Fire with Special Offers (KFSO):
Get $2 credit toward the purchase or rental of select digital movies in the Amazon Instant Video Store
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 December 9 and use the credit by Dec 17.
You might as well apply this one to your account right away, since it will apply automatically to any eligible purchase.