The process of using a virtual world (or any video game engine that has player characters) to make movies and video is called "machinima", a neologism that I hate. You can get a general overview of it from the FAQ page at the Academy of Machinima Arts. For a hilarious example of machinima, check out the "Red vs. Blue" series made using Halo soldiers.
The thing I filmed (Taped? So many of our terms are getting technologically obsolete. "Captured," perhaps) was a Trans Siberian Orchestra concert performed in SL by a very talented TSO tribute group, Rising Star Entertainment. I didn't plan to make a video, I just attended to enjoy the show. But as I watched and listened, I realized that still pictures wouldn't do a very good job of capturing the flavor of the event, and decided to try to get video.
I used a screen capture program called FRAPS as my recorder. To move my point of view smoothly, I used the Flycam function of my Space Navigator 3D "mouse" device. Once I had opened FRAPS and set a couple of things, the whole thing was as simple as hitting the F9 function key and then being a bit gentle with moving the camera with the Space Navigator.
FRAPS can capture audio too, which is great for recording a live performance like this one. I captured about three songs before Real Life intruded and I had to leave.
The next step was to edit the video. Editing is something that I love and dread...because, like creating a great retouched image in Photoshop, it is both a satisfying creative process and a very intense, all-absorbing one. My editing software is Sony's Vegas Pro, but you can use the free Windows Movie Maker and get good results. I took the three song clips that I'd recorded and picked the one I liked best. Then I chopped out the parts of the video clip that were not very good...unplanned, un-motivated camera moves, poorly lit bits, and the like...and filled the gaps with video snippets taken from the other song clips.
I also found that, unlike the Snapshot camera in the viewer, FRAPS records the entire screen, including any windows or HUDs that you happen to have open. As a result, I wound up doing a good bit of cropping to get a (relatively) clean set of images. Then I added titles and credits and saved the final version. While I was scratching my head and trying to figure out how I should render the final movie for uploading to YouTube, I discovered that the nice people at Sony had done my work for me. There was a button in Vegas for "Upload to YouTube". Wow, one button ease of use!
So I did, and you can see the result here: Trans Siberian Orchestra in Second Life