Hook your video output from your XBox to your VCR, or set top DVD Recorder (if you have one... if not, they're REALLY affordable), or the video input into your camcorder (preferably, a digital camcorder). Take note of the capability of your recording device... If you're going to record on an SD (Standard Definition) recording device, then you'll need to flip the switch on your XBox cable bundle to non HD.
If you're recording to a digital device such as a DVD recorder or a digital camcorder, then getting it to your computer is trivial. If you're recording onto a VHS tape, you're still going to need something to convert it to digital. I have a Hollywood DV/Analog bridge that does the trick. Be warned though, their support is non-existent... literrally. There are other devices you can get at Wal-Mart. I just checked their site, but can't find them there, but I see several variations of my old Hollywood DV/Analaog bridge every time I go there. They're pretty cheap too. With them, you plug your analog device (VCR, Camcorder, XBox) to your bridge and connect the bridge to either a USB or FireWire port on your computer and just import it directly into your computer. I recommend just using Windows Movie Maker (comes with Widows, so you already have it) to import it... don't need any extra software.
Alternatively, you can aim a video camera at an LCD monitor (don't even attempt a CRT as you'll get horrible vertical synching problems)... but then, if you want it as a video file, you've still got to go with one of the options above. TechTV (when it existed, before it was eaten, digested, excreted, and subsequently flushed by G4) recommended this low-tech method... They actually used it for their live TV demos. Their techs tested it and got the best quality doing it that way. I would imagine you get the best quality for TV that way, but the best for computer would be a purely digital reproduction of the original bits... but to do that, you'd need some screen capture software and when I try that, both it and the game are competing for CPU and if they aren't both winners, then frames will get dropped.
Hope that helps.