This offer is for those with a Kindle with Special Offers only. View the Special Offers on your Kindle (Menu, Special Offers) and you should see a new promotion (if you don't, turn on your wireless, click Menu, Sync & Check for New Items, then after the sync has completed, go to the Special Offers screen):
Spend $5 and get $5 in the Amazon Instant Video Store
Click on offer, then click on the link on the offer page sign up and get an email with the promotion code. Sign-up for this offer expires on September 21. You'll get an email (right away), a link to Special Offer page. There is no promo code on this one - once you have signed up, if you spend $5 on Instant Videos at Amazon before October 21, then you'll get a $5 credit, also for Instant Videos, deposited to your account sometime on or before November 21 (Amazon usually sends you an email a day or so later, to notify you of the credit).
This offer is limited to one per device AND one per customer (and, like all recent offers, is non-transferable).
There is no limit to the selection, so you essentially can rent $10 worth of instant videos at Amazon for half price. You can also use the promo on purchases, although there are not a lot of low-end movies, nothing says you can't buy a few episodes of a TV show or buy a full season or higher cost movie, that you were going to buy anyway, then get the credit. One good page to bookmark is the Instant Video Daily Deals page, where you can find links to the $0.99 and $1.99 daily/weekend rental deals, as well as any other Instant Video deals that Amazon is running. Keep in mind that the $5 is a true minimum - renting or purchasing a single item at $4.99 isn't "close enough"; with most pricing ending in .99, that essentially means you'd need to spend closer to $6 to take advantage of the deal. For those that rent Amazon's movies anyway, though, this is free money for your account.