This offer is only for those with a Kindle with Special Offers:
Get $2 off an award-nominated film at Amazon Instant Video
Click on offer, then click on the link on the offer page to receive an email with the promo code. Sign-up for this offer expires on February 26.
You'll get an email (right away), a link to the redemption page. This one works like a gift card and you need to apply the credit to your account first, before going shopping. Once you have entered the promotional code, you have until March 26, 2012. to complete your purchases.
I recommend that you apply the credit right away, since it works on any qualifying video purchase or rental - then you can shop on the web, from your Kindle Fire or your Roku (the XD and LT are currently $10 off, but the XS includes Angry Birds) and it will be used automatically.
You do have to be a bit careful - the link at the top of the redemption page sends you to the main Amazon Instant Video page; however, only those listed on the eligible titles will get the credit applied.