Well, I have no experience on this matter so I can't be sure, but there are a lot of different methods and devices to record your Xbox 360 gameplay if your computer does not have a built in capture card. You can use external capture cards, USB capture devices, and even your home DVD recorder. The only thing I can recommend is a VGA box for high quality. This page has a complete how-to of recording gameplay from your x-box 360. It can help you way more than I can.
How to Record Xbox 360 Gameplay. Guides, Videos, and Information.