How to Be Undetected on Facebookby Aaron Parson
If you want to look up Facebook members, use Facebook apps or participate in a Facebook group, you'll need a Facebook account. Set your privacy options to the strictest levels to prevent sharing your personal information. To keep people from detecting you on Facebook, don't post comments or "like" posts in public areas. If you don't want people on your Facebook friends list to know when you're online, log out of Facebook's chat feature.
Change Your Privacy Options
Click the gear icon at the top of your Facebook Timeline or news feed and select "Privacy Settings." For the highest security, set "Who can see your future posts?" to "Only Me." Change "Who can send your friend requests?" to "Friends of Friends." Set the options to find your profile through your email address and phone number to "Friends." Turn off search engine indexing to hide your profile from Google and other Web searches. Your privacy settings only apply to posts on your own Timeline, so don't make comments on other users' posts if you want to stay hidden.
Log Out of Chat
Facebook chat shows people on your friends list when you log on Facebook, allowing instant communication. When you turn off chat, no one knows whether you're currently using the site. Click "Chat" in the lower right corner of any page on Facebook to display the chat bar. Press the gear icon on the bar and pick "Turn Off Chat." Chat remains disabled between Facebook sessions until you turn it back on.