How can I edit my video in this way?

You need to use an alpha channel, which allows you to have multiple video tracks running simultaneously.

The iPod screen is basically a frame and the video you want to play is resized to fit into the smaller space for the screen.

How you do this depends on the software you are using. It could even get as complex as pinning the video to the screen if the iPod screen is not in a static position, but this would take more work.