You have to connect your computer to a DVD recorder. So it depends on what kind of output you have available on you computer.
For example, my desktop equipped with an ATI All In Wonder video/graphics card can output via s-video.
Some have composite.
Some have HDMI.
Some have nothing at all.
The DVD recorder also needs to accept that kind of input, either directly or via an adapter.
In terms of non-technical ease, this honestly isn't any easier than a program would have been. But no program exists to both rip and convert this.
Amazon simply does not want users to download its video, same as Hulu, and right now there's nothing to be done about it. If ever it does become possible, it'll likely be unofficial/unlicensed methods that often carry a heavy tech learning curve. A year ago, you could download Hulu streams, but it was fairly techie to do.
Another option is to hook up two computers -- one to play, one to capture. But again, it depends on what you have available.