Instructions
Log in to your Xbox Live account.
Press the "Guide" button on your Xbox 360 controller. This is the main, middle button on your controller that lights up during game play. Press it to bring up the Guide menu.
Scroll to the right over to the "Settings" menu. Select "Preferences," then "Online Status."
Select "Busy" from the Online Status settings menu. This will show others logged in to Xbox Live that you are "Busy." It acts like a "Do Not Disturb" setting for your Xbox Live account.