
The following two tutorials provide step-by-step instructions exactly how to do such using FileLab and VSDC video editors. As usual, these programs are both 100% full working freeware, with no strings attached. More info on these and others freeware editing programs may be found here. And here are the tutorials:
FileLab "Picture in Picture" Editing (download FileLab here)
This video is in HD. Click "Full Screen" in lower right corner.
This video is in HD. Click "Full Screen" in lower right corner.
Please note that I apologize for the quality of the following video, and also the singing. I was rushed, I'm not a singer, and I used the microphone from a cheap $4 webcam. But the video does show that it is easy to import multiple simultaneous PIP videos with this program.
VSDC "Picture in Picture" Editing
Note that VSDC downloader will suggest installing additional bundled software along with VSDC. This is why VSDC is free. Carefully read those installation screens and make sure to uncheck or decline any software that doesn't interest you (probably all).
If you're interested in doing music covers, of the two programs, I highly recommend that you consider VSDC. It does take some practice. But it's well worth taking the time to learn it, as it was used in the following projects (and you can't beat the price :).