She is using Chroma Key to create this effect.
She shot one video of herself in front of a green screen, then used Chroma Key to make the green background transparent so that she could overlay it on another video of herself.
I walk you through how to do this, step by step, in the "Cool Tricks & Hot Tips" book for Premiere Elements. (You may also be able to find more information on it online.) It's not a terribly complicated process -- but you need to get the details right.
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Look for Chroma key or Green Screen in the help or google it. There is a heap of info on the subject.
Also if you want say the same person on either side of the screen talking to each other you can simply shoot both scenes without moving the camera or changing the lighting in any way, put each clip on different tracks and split screen between the two clips.
Great suggestion, Ted!
Here's an example I created for my "Cool Tricks" book using the Matte tool and three videos shot of the same scene.
It's not quite as clean as it should be -- but you get the principle. Did it in about 20 minutes.