How to Log in Unnoticed on Facebook
If you have a Facebook account and a large friends list, it's almost inevitable that at least one will start messaging you as soon as you sign on. If you want to sign in to Facebook to browse without being messaged by multiple friends, you can set your Facebook chat to "offline." Because that's the only way friends can see whether you're logged in, you can be on Facebook without people knowing. When you log out of Facebook chat, you will not show up as online until you manually re-enable chat.
Log in to your Facebook account.
Click on the "Chat" button in the bottom-right of the menu.
Choose "Go Offline," then log out and log in again. This will keep friends from seeing you when you log in until you manually change the setting.