Yes, you layer the two video clips on top of each other, and you need editing software that allows you to mask out (cut away) half of the top video layer, so that the bottom video shows through.

I'm sure there are plenty of free apps that will let you do this. Commercial apps that can do this well are, for example:

Adobe Premiere, Sony Vegas for Windows.
Final Cut Pro X, or Adobe Premiere for Mac. I think even iMovie can do it, but I'm not sure.