Instructions
Scroll to the "System Settings" option on the Xbox 360's main menu and press the "A" button. This option is located on the far right of the "My Xbox" list.
Move the cursor onto the "Console Settings" option and press the "A" button.
Scroll down to the "System Info" option, which should be the last option on the list. The IP address will be displayed on the right side of the screen and is clearly labeled with the phrase "IP."