While the PlayStation Network (PSN) lets you do battle with your friends, download demos and older games, there's no reason to remain signed in when you are not using the service. Signing out of the PlayStation Network is a bit simpler than signing in; there's no need to enter your username or password. One button on your controller is all it takes to go offline.
Move the analog stick to the right, until you reach the blue "PlayStation Network" icon. The icon is sandwiched between the "Network" icon and "Friends" icon.
Press the "Triangle" button on your PlayStation controller. Move down to the "Account Management" icon, which is the first icon under "PlayStation Network."
Press down to select "Sign off." Press the "X" button on your controller. You will return to the "PlayStation Network" list of options. You should see "Sign in" above "Account Management." This indicates you are completely signed off of the PlayStation Network.