Nothing fancy, just the software that came with my webcam (a mid-level logitech model). It records in HD, but doesn't have any bells and whistles.
I also use a $5 directional lamp I bought at Target, so the lighting would be passable.
[edit] Am I crazy, or did you change your question? It's possible that I somehow misread you, so I'll respond again!
It's not hard, just a bit time-consuming. I use webcam software that makes it pretty easy to time the start of my recording to the exact moment the video I'm playing starts. If you have those lined up properly from the start, it's very easy.
In terms of editing software, I use this:
Windows Movie Maker 6 (not the new version with Windows 7/8, as that has fewer useful features):
http://movies.blainesville.com/2010/05/ ... 60-on.html
And this guy's FX pack to do Picture in Picture:
http://www.rehanfx.org/
(Even after the trial officially ends, the FX pack still works.)
It's a little wonky, but this guy gives a decent tutorial:
http://www.youtube.com/watch?v=9ax-qh9k1ic
Apparently, some of that won't work with Windows Vista, but it works fine for me with Windows 7/8.