Instructions
Turn on the Xbox 360 and wait for the main menu or "Dashboard" to load fully. Move the analog stick to the right and select the "System" tab by pressing "A" on the controller.
Select the "Memory" tab by pressing "A" again and select the "Xbox 360 Hard Drive" storage device. The system will display a list of all data stored on the console's hard drive. Select "Player Accounts" and choose the profile you wish to delete from the Xbox by pressing "A."
Select "Yes" and press the "A" button on the controller when the system asks you if you really wish to delete the account from the hard drive. The console will delete the profile and all associated content from the hard drive, and you will be able to use the Xbox again as soon as the deletion process is complete.