First Mark recorded his guitar track, I believe he used a Canon Vixia HG20 HD camcorder (amazing quality by the way) using the built-in mic on the camera. He played along with headphones, listening to the original Beatles song.
He then sent that video file to me.
I recorded my guitar track while listening with headphones to his guitar track. I recorded my video with my Kodak Zi8 video camera and recorded the audio separately from the video using Garage Band on my MacBook Pro. I used a combination of a microphone (Audio Technica AT2020 Cardioid Condenser Microphone) and the 1/4" Fishman AG under saddle guitar pick-up that I had installed in my Breedlove AD200SM. I have both the microphone and the pick-up plugged directly into my Presonus Firebox Direct-In box. This box has two XLR mic and/or two 1/4" line TRS inputs and 48v phantom power to power the condenser mic. It also includes a good quality pre-amp to really warm up the vocals and guitar. The Firebox is connected to my MacBook Pro via a firewire cable. Now with all of the inputs getting into my MacBook Pro, I use Garage Band to record everything. I won't go into all the details of Garage Band but it's a really slick and easy interface for recording multiple tracks at once or independently and gives you a multitude of varying software or virtual instruments, such as drums and keyboards and music loops etc.
So... basically, I recorded myself playing to Marks track in this manner. I had the video camera running at the same time, but I only used the video portion and not the audio from the camera, more on that later.
Once I had my guitar track finished, I took Marks guitar track and my guitar track mixed together in Garage Band, and played that in my headphones while I recoded my vocal portion (in the same manner as above, using the AT2020 mic).
Once my guitar and vocal portion were done, I sent this audio file to Mark which now included all three parts. He then listen to this in his headphones while recording his vocal part. He used his camcorder to record the video of him singing but he used a regular XLR type mic plugged directly into his computer using Audacity on his PC to record the audio. So basically he recorded the video and audio at the same time but recorded the audio independently via the microphone as well. Then he sent me both of these files, the video and the audio separately. (I would eventually strip out the audio portion within the video file)
So... now I have all the piece, all the audio tracks independently and all the video tracks independently. Now comes assembly time. I go back to Garage Band bring in all the audio tracks, Marks guitar, my guitar and both our vocals. They are all on separate tracks independent of each other so I have control over the sound of each one, volume, pan, effects, timing, etc. Once I have all the tracks synced up, timing wise, I can continue to play with the sound and levels and stuff. I also used Garage Band to put in the drum track. Because our timing and tempo where not stellar, it was painstaking to adjust each beat to match our playing, which is evident in the song.
It's usually customary to put in, or record to, a drum track "first" and then play to that to be sure you're in time, but the drum track was an after thought and I'm a Pollock anyway so it worked out OK. 
So now the audio portion of the song is done.
Now comes Final Cut Express, video editing software. Since we each used our camcorders to video ourselves playing the audio parts, theoretically the video parts should match the audio parts great. And for the most part they do.
In Final Cut I imported the finished audio track, which is now mixed down to just one single file on one track inside the video software. I proceeded to drag in each video track to its own track and started syncing each one to the music that's playing, by sliding each video track left or right accordingly to the song timeline. There are usually enough visual queues in the video tracks to get it syn'd up pretty well. As for the 4 window multi-cam picture in picture thing, that is just a cropping, scaling, and positioning feature that Final Cut offers you. You can select a video track or part of a video track and scale it and move it to a position it on the screen. I just did this for each video and moved them appropriately, the soft edges are just another built in effect. This is barely even scratching the surface of what Final Cut is capable of, but I felt this was clean enough visually and appropriate.
And voila!
Did I miss anything? For those of you that stuck with this read, Bravo, pizza for you!
Really though, I love this stuff, I'd be happy to help anywhere I can.
And you're right, if you're gonna use a virual drummer, have it go first (and then try to keep up with it - it's still hard to do!). -Daryl