How to Log Out of Your Account on an iPod Touch
If you plan on making full use of your iPod touch, you need an Apple ID. A free Apple ID account allows you to make purchases in the iTunes application, App Store and sign in to the game center. Once you log in with your Apple ID on the iPod touch, you remain logged in until you manually sign out. Sign back in with the same or a different Apple ID to continue using programs that require it.
Tap the gray "Settings" icon, located on the iPod touch home screen.
Scroll down and tap the "Store" icon in the menu.
Tap your Apple ID, usually an email address.
Select "Sign Out" in the pop-up window.