You mean you and yourself on the sofa? You don't need AE for that. A free video processing app like VirtualDub can do that, assuming there's enough spacial separation to provide a clean edge in the middle. As for the rest - why not simply try? Adobe offer trial versions of all their products and while the install may be a pain in the neck at times, those 30 days should siufficiently allow you to get a feel for everything, especially when you follow the extended links from the online help to a selection of tutorials and additional helpful pages.
So, it's basically 2 videos but one is cut in the middle and the other one is superimposed on it and shows what's left?
Still, how would you be able to do that in After Effects or Virtual Dub?
In After Effects you would use a Mask to isolate the foreground mandolin-guy.
But as Mylenium said, After Effects is potentially overkill if you just want it do what's seen in your example. Most non-linear editing applications (like Premiere Pro) offer masking tools.
If the foreground guy's mandolin moved in front of the guitar guy, however, that would become a much more difficult masking situation - each frame would need to be "traced" with the mask, essentially cutting him out. That's where After Effects would be the better tool for the job.
So Premiere Pro will do the same thing and is cheaper?
Also, is the correct method of doing this called "masking"?
(I'm a complete n00b which is why I asked if it's difficult to do or which tools to use -- still haven't received a specific answer for that though.. :-( )