I don't do this, but it looks like what you need is the free Amazon Instant Video app from the App Store .
I don't know if it will let you stream to the Apple TV. If it can, it will probably be through AirPlay. If not, I can't find any other way to get Amazon Prime on an Apple TV. There were rumors of Amazon working on their own TV box, so they may be blocking or delaying Apple TV support for that reason.