Instructions
Turn on your Xbox 360. The console should automatically sign you in to Xbox Live. Scroll up to "My Xbox" on the left side. Move one box to the right and click your Xbox Live profile.
Scroll to the right, to "Account Management." Click "Manage Account." Scroll to the right again, until you reach the "Your Information" box. Click "Windows Live ID."
Highlight "Windows Live ID" and press "A" on your controller. Click "Yes." Press "A" and use the on-screen keyboard to type in the password for the email address currently attached to your Xbox Live account.
Click "Done." Type in your Windows Live email address and password in the appropriate text boxes. Click "Sign in," then click "Yes, Change." The Xbox 360 will confirm the change and ask if you wish to save your new password to the console.