You shouldn't use Windows Media Centre, that's just terrible.
Instead, you should head to Windows Media Player. You should click "Streaming" in the upper left corner and head to the settings. There you can add your Xbox 360 to your network. Then when your computer/laptop is turned on (NOT stand-by) it will start to sync the music (and/or videos and images). This could take a couple of minutes.
After that, you can always play music on your Xbox 360 via the Guide Button in-game, as long as your computer/laptop is turned on.