What is the best method to record a home video of multiple players?
Here is what I do (for my videos on http://www.youtube.com/user/killergege).

Tools : 


Software : Reaper for audio recording, Sony Vegas Pro for video editing
Hardware : a camcorder, an audio interface (POD HD500 in my case)


Process :


I create a new project in Reaper and Vegas and setup everything to record audio properly on Reaper through my audio interface.
I add a backing track in Reaper.
I record myself playing each instrument (video &amp; audio) at the same time, Reaper takes the sound, the camcorder takes the video. I might do several takes, Reaper handles pretty well takes and the camcorder just keeps recording.
When finished recording I then have a track for each instrument in Reaper (with maybe several takes in each track), and a video for each instrument.
Then I select the audio takes and mix the tracks with the backing track (changing volume, adding fades, etc.)
I export the audio mixed and import it in Vegas
Then I edit the videos in Vegas, cutting the unused takes and mixing with effects (I use chroma keying to remove the background, fades, camera movements) and to place the videos like you want. Editing the video to do a "splitscreen" like in the example is quite easy and a lot of other editing software can do that.
The hard part is syncing the audio with the video. I try to sync the videos' audio with the Reaper mixed audio I imported just before removing the videos' sound.
I also do it visually (trying to match hand movements with audio).


If you need more details, just ask.