This offer is only for those with a Kindle Fire with Special Offers (KFSO).
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. At the bottom, you should see the offer for $3 to spend on Select TV Episodes. 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 must sign up by October 11.
Unlike the previous offer, you can't choose from the entire Instant Video Store, but must use the credit for "television episodes" (rentals and purchases). 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. The credit expires October 18, so be sure to use it quickly.
I'm not sure what (if anything) I'll spend this one. I do wonder if it will work on buying an entire season for a series.