You could run Camtasia to record the screen when playing the video game. This is a common tool to create a video from what's happening on the screen. If you have a slower machine, it will be a monster headache.
If you're running a PC game check to see if it does in-game recording to an AVI or MPG or MOV file. Or maybe it will frame-capture to BMP or TGA. Either option will give you something to load up into Vegas for editing. Another option is to run the VGA signal to a down-converter, making it NTSC and then recording that through your DV camera or digitizing card.
If it's a console game you should be able to just plug the AV output jacks right into your camera or card.
Camtasia is a deadly piece of software and probably will NOT work for this. A guy in the office down the hall just tried making UT2k3 demo videos w/ Camtasia and they, well, sucked. Quality was alright, if 8 frames per second is your thing. Best bet is get a tool like Fraps, I think it's called, which is a shareware, high-level game demo recorder. Many games, including Half Life, Quake 1-3, and UT?, have demo video capture modes. You just hit F9 or something and voila. It varies game to game. A lot of this is going to depend on your RAM, willingness to burn disk space, and video card, but good luck!
quake3 games support a console command to dump image sets of what is on screen.. cl_avidemo is the command, followed by a number representing what fps you want. eg.. cl_avidemo 25. Change the number to 0 to stop dumping frames. Unfortunately vegas 4 doesn't import .tga files, so you will need to look at converting them into a format that vegas does support. Virtual Dub (freeware) is ideal.
Other games engines support similar frame dumping to screenshots, failing that use fraps, as suggested. Fraps also performs audio dumping, apparently.