Your questions: how do I connect an Xbox 360 to my Windows PC?
A question from an Xbox 360 owner with a Media Center PC: "how do I connect an Xbox 360 to my Windows PC?"
For the latest info, see this article on xbox.com on connecting your PC up to an Xbox 360 with Windows Media Connect. If you are connecting an Xbox 360 to a PC running Windows Vista Home Premium or Windows Vista Ultimate, then take a look at this article on microsoft.com. (I did reference blog about the Xbox 360 as a Media Center Extender previously with a link to Chris Turkstra's Expert Zone Support WebCast.)
And if a picture is worth a thousand words then a video is, well, worth a few more than that:
If you have a firewall on your home network, you may need to open up specific ports - see also http://support.microsoft.com/kb/911728.